Daily Papers

On-Policy Self-Distillation (OPSD) has become a standard post-training approach for improving visual reasoning in multimodal large language models (MLLMs). Existing methods draw privileged information from diverse input sources to guide self-distillation. Yet these designs overlook Modality Imbalance, a challenge inherent to MLLM reasoning. When textual information dominates generation, the model cannot fully integrate its multimodal input. Consequently, carefully designed privileged information remains underused, limiting the effectiveness of OPSD. To examine this limitation, we construct a Positive Teacher with the Zoom-In Image and a Negative Teacher with the Mask Image, which exhibit different degrees of Modality Imbalance. Changes in their reasoning correctness and token logits reveal that Modality Balance can itself serve as privileged information. Motivated by this finding, we introduce OPD-V, a visual OPSD paradigm that instantiates such information through the Positive Teacher and Negative Teacher. Positive Modality-Balance Logits Margins define a Modality-Balance Trust Region that selects the on-policy tokens used for self-distillation. Experiments across 6 benchmarks, 4 MLLM backbones, and 5 post-training methods show that OPD-V consistently improves reasoning performance while reducing training cost.

Unified multimodal models (UMMs) interleave generated ''visual thoughts'' (VTs) with text reasoning to improve spatial tasks. This incurs roughly an order-of-magnitude inference cost from multi-step diffusion. We find this cost yields limited direct benefit. On ThinkMorph, removing or noising VTs barely changes accuracy across nine benchmarks. Once rendered, attention concentrates on the VT regardless of content. Yet a KL diagnostic shows that conditioning on a privileged VT trace shifts the model's completion distribution. This suggests the generation pathway encodes useful reasoning beyond the rendered pixels. Motivated by this gap, we propose Visual On-Policy Self-Distillation(Visual-OPSD). Teacher and student share identical weights but differ in context: the teacher sees privileged VTs while the student sees only the question. Token-level JSD distillation on on-policy student trajectories transfers the teacher's reasoning to a text-only student. Across nine benchmarks, Visual-OPSD improves over its generative teacher by +3.40pp with 14.3times speedup (10.0s vs. 142.8s per sample) and outperforms same-scale VLMs by +63.83pp on VSP. A Gaussian-noise control (+0.40pp vs. +10.28pp for real VTs) and 58.4% closure of the KL gap confirm that gains come from the semantic content of the generation pathway.

Vision-language models (VLMs) have made substantial progress in long-video understanding, with standard backbone models typically answering questions from frames sampled across the full video. However, as videos become longer, the full-video context inevitably contains more question-irrelevant temporal content, which can distract the model from the evidence needed to answer a specific question. We empirically find that focusing the visual input on short annotated clue intervals containing question-relevant evidence consistently improves prediction accuracy across model scales compared with using the corresponding full videos, while requiring fewer input frames. Based on this finding, we introduce Clue-OPSD, a clue-privileged on-policy self-distillation framework for long-video understanding. During training, a full-video student learns from a self-teacher conditioned on the corresponding clue interval by aligning their next-token distributions along student-generated trajectories. Clue-OPSD thus uses clue intervals as privileged supervision without relying on ground-truth answer labels, while requiring no clue annotations or additional modules at inference time. Extensive experiments across multiple long-video understanding benchmarks and Qwen3.5 model scales demonstrate consistent improvements over the corresponding backbone models and strong performance against supervised post-training baselines.

''Thinking with Images'' has emerged as an effective paradigm for fine-grained visual reasoning: by explicitly zooming into relevant regions and reasoning over crops, models can access local evidence that is difficult to recover from a single global image. However, this benefit comes with redundant tool invocations and longer inference traces. Moreover, when such behaviors are learned mainly from outcome reward, the resulting intermediate crops or visual cues can be noisy or fail to faithfully capture task-relevant visual evidence. In this work, we ask whether the reasoning benefits of ''Thinking with Images'' can be internalized through Thinking with Imagination: an internal process that decides where to look and imagines what visual cues closer inspection would reveal without actually invoking tools. We propose Imagine-OPD, an on-policy self-distillation framework in which a teacher plays the role of a ''Thinking with Images'' reasoner during training: it receives privileged zoomed evidence views derived from annotated regions, and supervises the model's own imagination reasoning trajectories. Imagine-OPD does not require an external teacher or high-quality imagination demonstrations. Experiments on vision-centric benchmarks show that Imagine-OPD achieves the best average performance among compared models while significantly reducing inference overhead compared with ''Thinking with Images'' methods.

Visual on-policy distillation relies heavily on an informative teacher-student asymmetry, through either a larger, stronger teacher or privileged supervision, such as reference answers or ground-truth regions of interest. This raises a fundamental question: where can informative asymmetry come from when nothing privileged is available? We answer this by inverting where the asymmetry comes from. Rather than adding privileged information to the teacher, we subtract information from the student. This asymmetry creates the same effective learning signal for free as a teacher with access to information unavailable to the student, without ground-truth annotations, rewards, or a separate stronger teacher model. Building on this principle, we introduce Self-Supervised Visual On-Policy Distillation (S^2VOPD), a simple yet effective method that constructs on-policy learning signals from asymmetric augmented views. S^2VOPD distills the teacher's distribution conditioned on the original image on-policy into the student distribution conditioned on a strongly augmented view of the same image. We systematically explore a broad design space of visual augmentations and uncover that (1) asymmetry matters: all four augmentation families improve performance, while symmetric self-distillation degrades it; (2) strength matters: performance peaks at a moderate strength; and (3) the gap must remain task-consistent: augmentations that completely remove the question-relevant evidence can induce large but uninformative discrepancies. Across six fine-grained perception benchmarks, S^2VOPD improves Qwen3.5-4B from 70.7% to 77.4%, above all open-source models compared, up to Qwen3-VL at 235B, and surpasses GPT-5.4. While holding training data the same, it recovers 96% of the improvement achieved by methods with privileged information. Website is at https://williamium3000.github.io/s2vopd

We propose OPSD-V, an on-policy self-distillation paradigm for post-training few-step autoregressive (AR) video diffusion models. Existing few-step AR video generators can produce long videos with low latency, but still suffer from error accumulation and weakened motion dynamics during long autoregressive rollout. OPSD-V reduces long-horizon degradation while preserving the original few-step inference path. The key idea is to introduce real long-video data as temporal context during training and use it to provide dense trajectory-level supervision. Specifically, the student follows the exact inference-time rollout, generating each chunk conditioned on its own previously generated KV cache. In parallel, the teacher is evaluated at the same student-visited denoising states, but uses a cleaner AR-consistent temporal cache in which older history can be replaced by real-video context. This provides dense denoising-level corrective targets under on-policy AR cache dynamics, without changing the sampler, number of denoising steps, or inference-time cache mechanism. We apply OPSD-V to representative few-step AR video models, including Self-Forcing and LongLive. Experiments show consistent improvements in visual quality, motion dynamics, and VBenchLong scores. A user study with 10 participants comparing 20 video pairs shows that OPSD-V is preferred over the base models in 66.0% of overall-preference judgments (82.5% excluding ties).

Multimodal Large Language Models (MLLMs) still struggle with fine-grained visual understanding, where answers often depend on small but decisive evidence in the full image. We observe a regional-to-global perception gap: the same MLLM answers fine-grained questions more accurately when conditioned on evidence-centered crops than on the corresponding full images, suggesting that many failures stem from difficulty to focus on relevant evidence rather than insufficient local recognition ability. Motivated by this observation, we propose Vision-OPD (Vision On-Policy Distillation), a regional-to-global self-distillation framework that transfers the model's own privileged regional perception to its full-image policy. Vision-OPD instantiates two conditional policies from the same MLLM: a crop-conditioned teacher and a full-image-conditioned student. The student generates on-policy rollouts, and Vision-OPD minimizes token-level divergence between the teacher and student next-token distributions along these rollouts. This enables the model to internalize the benefit of visual zooming without external teacher models, ground-truth labels, reward verifiers, or inference-time tool use. Experiments on multiple fine-grained visual understanding benchmarks show that Vision-OPD models achieve competitive or superior performance against much larger open-source, closed-source, and "Thinking-with-Images" agentic models.

On-Policy Self-Distillation (OPSD) uses privileged information available only to the teacher to provide dense token-level supervision on trajectories generated by the student. However, existing methods often rely on verified solution traces, explanations generated by external models, or manually localized visual evidence, which limits their scalable application to multimodal large language models. To address this issue, we exploit the information gap between high- and low-resolution views of the same image and propose RP-OPSD (Resolution-Privileged On-Policy Self-Distillation for Multimodal Large Language Models). During training, the student policy generates on-policy trajectories from images at one-quarter of the original resolution, while the teacher policy provides supervision using the original-resolution images. By minimizing the divergence between their output distributions along the student trajectories, the student learns the predictive behavior of the teacher under high-resolution inputs, thereby strengthening its low-resolution capability and transferring the learned improvement to original-resolution inference. RP-OPSD requires neither additional human annotations nor external models to generate solution traces but only image--question pairs. Experiments on Qwen3.5-9B show that RP-OPSD achieves a 5.45\% relative improvement in average performance at the original resolution and a 1.78times training speedup over OPSD. These results demonstrate that resolution differences can serve as a simple and scalable source of privileged information, providing an effective and efficient approach to on-policy self-distillation for multimodal large language models.

Graphical User Interface (GUI) grounding maps natural language instructions to the visual coordinates of target elements and serves as a core capability for autonomous GUI agents. Recent reinforcement learning methods (e.g., GRPO) have achieved strong performance, but they rely on expensive multiple rollouts and suffer from sparse signals on hard samples. These limitations make on-policy self-distillation (OPSD), which provides dense token-level supervision from a single rollout, a promising alternative. However, its applicability to GUI grounding remains unexplored. In this paper, we present GUI-SD, the first OPSD framework tailored for GUI grounding. First, it constructs a visually enriched privileged context for the teacher using a target bounding box and a Gaussian soft mask, providing informative guidance without leaking exact coordinates. Second, it employs entropy-guided distillation, which adaptively weights tokens based on digit significance and teacher confidence, concentrating optimization on the most impactful and reliable positions. Extensive experiments on six representative GUI grounding benchmarks show that GUI-SD consistently outperforms GRPO-based methods and naive OPSD in both accuracy and training efficiency. Code and training data are available at https://zhangyan-ucas.github.io/GUI-SD/.

On-policy self-distillation (OPSD) trains a model on its own rollouts and uses a frozen copy to provide dense token-level targets conditioned on a reference target. This works well for LLM reasoning, but a direct extension to multimodal large language models (MLLMs) can create a shortcut: the privileged target may guide tokens mainly based on the text reference target rather than the image. We propose ViGOS, a visually grounded OPSD framework for MLLM post-training. The student first writes a visual description and then reasons toward the final answer. For valid rollouts, an image-only perception teacher supervises the description, while a privileged reasoning teacher supervises the reasoning and final answer on the same student prefix. A reference teacher is used only for invalid rollouts to recover the output format. Across general vision-language, expert reasoning, visual math, spatial grounding, and visual-language-prior benchmarks, ViGOS keeps the main benefits of OPSD and improves image-grounded behavior in shortcut-prone settings.

On-policy self-distillation (OPSD) is promising as it removes the external teacher required by on-policy distillation (OPD), yet it still needs asymmetric information between teacher and student to ensure that the self-teacher provides a stronger learning signal than the student. Existing methods create this asymmetry either through privileged answers or visual evidence. We ask whether both can be removed, yielding a simpler form of OPSD driven purely by input conditioning. For this purpose, we propose Visual Contrastive Self-Distillation, namely VCSD, which converts image-content removal into an on-policy self-distillation signal. At each student-generated response prefix, the EMA teacher produces two next-token distributions under the same prompt and prefix -- one conditioned on the original image and the other on a content-erased control. Their token-wise log-probability difference highlights candidates whose likelihood is specifically increased by the instance-level visual content. We use this contrast to sharpen the teacher's original-image distribution within its plausible support, and distill the resulting full-distribution target into the student. Using ViRL39K dataset, VCSD consistently outperforms matched OPSD across Qwen3-VL and Qwen3.5 models. For example, on Qwen3-VL, it improves the seven-benchmark aggregate from 62.27% rightarrow 67.04% at 2B, 71.30% rightarrow 73.16% at 4B, and 72.51% rightarrow 76.26% at 8B. Furthermore, VCSD requires no external teacher, privileged answers, visual evidence signals, reasoning traces, or additional inference-time cost.

Open-ended image generation is no longer a simple prompt-to-image problem. High-quality generation often requires an agent to combine a model's internal generative ability with external resources. As requests become more diverse and demanding, we aim to develop a general image-generation agent that can self-evolve through trajectories and use tools more effectively across varied generation challenges. To this end, we propose GenEvolve, a self-evolving framework based on Tool-Orchestrated Visual Experience Distillation. In GenEvolve, each generation attempt is modeled as a tool-orchestrated trajectory, where the agent gathers evidence, selects references, invokes generation skills, and composes them into a prompt-reference program. Unlike existing agentic generation methods that mainly rely on image-level scalar rewards, GenEvolve compares multiple trajectories for the same request and abstracts best-worst differences into structured visual experience, provided only to a privileged teacher branch. Inspired by on-policy self-distillation, Visual Experience Distillation provides dense token-level supervision, helping the student internalize better search, knowledge activation, reference selection, and prompt construction. We further construct GenEvolve-Data and GenEvolve-Bench. Experiments on public benchmarks and GenEvolve-Bench show substantial gains over strong baselines, achieving state-of-the-art performance among current image-generation frameworks. Our website is as follows: https://ephemeral182.github.io/GenEvolve/

Large multimodal models (LMMs) have demonstrated strong OCR recognition capabilities, yet remain vulnerable to adversarial visual text that is readable to humans but challenging for models to localize and recognize. Existing OCR benchmarks mainly focus on natural or document-style text, while adversarial OCR evaluations remain limited in scale, task coverage, or region-aware evaluation. In this paper, we formulate adversarial OCR as a grounded OCR perception task and introduce AdvSpot, the first benchmark for grounded adversarial OCR evaluation. AdvSpot comprises 390 images with region-level annotations, spanning 5 primary categories and 13 fine-grained adversarial OCR types. To address this challenge, we propose ArmorOCR, a two-stage training framework for robust adversarial OCR perception. ArmorOCR first acquires missing adversarial OCR perception from privileged transformed observations through On-Policy Self-Distillation (OPSD), and then refines grounded OCR perception through Group Relative Policy Optimization (GRPO) with task-conditioned rewards for localization, recognition, full spotting, and visual question answering (VQA). Experiments on our AdvSpot, other adversarial OCR benchmarks, and general OCR benchmarks demonstrate that ArmorOCR consistently improves adversarial OCR perception while preserving competitive general OCR capability.

Self-improvement for multimodal large language models (MLLMs) is typically driven by reward-based methods that provide only coarse scalar feedback. Distillation offers a richer alternative through dense token-level supervision, but in the visual domain it usually depends on privileged context constructed using external annotations and tools, or stronger models. We introduce CVPD (Contrastive Counterfactual Visual Process Distillation), which, to the best of our knowledge, is the first fully self-contained framework for dense, on-policy, token-level visual self-distillation for MLLMs. CVPD identifies visual blind spots where zooming into a region changes and sharpens the model's answer distribution, while removing the same region leaves the full-image behavior largely unchanged. Such regions reveal perceptual information that the model can encode but fails to consistently utilize under full-image conditioning. We propose a three-gate Counterfactual Criterion that identifies these regions directly from the model's own responses and converts them into dense contrastive supervision for self-distillation. On Qwen3-VL-8B-Instruct, CVPD outperforms six self-evolving baselines across twelve benchmarks, including methods that rely on external GPT-4o supervision, without a single regression. It achieves gains of +3.60 on OCRBench, +3.38 on MMStar Fine-Grained Perception, and +3.08 on MMStar Logical Reasoning, while maintaining or improving performance on broader multimodal benchmarks.

While vision-language models excel at general multimodal understanding, they still struggle with visual spatial planning. We attribute this to a perception-reasoning modality gap: visual planning requires models to infer latent state structures from pixels and then reason over the recovered structure to produce valid actions, whereas symbolic planning directly leverages explicit objects and constraints. This creates dual bottlenecks in visual state recovery and multi-step planning. To address this, we propose MGSD, a two-stage modality-gap-aware self-distillation framework. First, a cold-start grounding stage equips the visual student with reliable state representations, minimizing early perception noise. Second, a privileged teacher transfers planning capabilities via on-policy distillation, using explicit symbolic states to supervise the student's own visual rollout prefixes. Crucially, symbolic data is used strictly during training, leaving inference purely visual. Experiments on visual planning benchmarks show that MGSD consistently improves visual planning across both 4B and 8B backbones, raising the macro average by 19.3% and 18.4%, respectively. The resulting models narrow the gap to symbolic-input upper bounds, while ablations and diagnostics confirm that the improvement comes from both visual state recovery and optimal-path reasoning. These results suggest that modality-gap-aware self-distillation improves not only how models perceive actionable states, but also how they plan over the inferred structure. Code is available at https://github.com/Oranger-l/MGSD.

Real-time video generation via diffusion is essential for building general-purpose multimodal interactive AI systems. However, the simultaneous denoising of all video frames with bidirectional attention via an iterative process in diffusion models prevents real-time interaction. While existing distillation methods can make the model autoregressive and reduce sampling steps to mitigate this, they focus primarily on text-to-video generation, leaving the human-AI interaction unnatural and less efficient. This paper targets real-time interactive video diffusion conditioned on a multimodal context, including text, image, and audio, to bridge the gap. Given the observation that the leading on-policy distillation approach Self Forcing encounters challenges (visual artifacts like flickering, black frames, and quality degradation) with multimodal conditioning, we investigate an improved distillation recipe with emphasis on the quality of condition inputs as well as the initialization and schedule for the on-policy optimization. On benchmarks for multimodal-conditioned (audio, image, and text) avatar video generation including HDTF, AVSpeech, and CelebV-HQ, our distilled model matches the visual quality of the full-step, bidirectional baselines of similar or larger size with 20x less inference cost and latency. Further, we integrate our model with audio language models and long-form video inference technique Anchor-Heavy Identity Sinks to build LiveTalk, a real-time multimodal interactive avatar system. System-level evaluation on our curated multi-turn interaction benchmark shows LiveTalk outperforms state-of-the-art models (Sora2, Veo3) in multi-turn video coherence and content quality, while reducing response latency from 1 to 2 minutes to real-time generation, enabling seamless human-AI multimodal interaction.

On-policy distillation (OPD) has become a popular training paradigm in the LLM community. This paradigm selects a larger model as the teacher to provide dense, fine-grained signals for each sampled trajectory, in contrast to reinforcement learning with verifiable rewards (RLVR), which only obtains sparse signals from verifiable outcomes in the environment. Recently, the community has explored on-policy self-distillation (OPSD), where the same model serves as both teacher and student, with the teacher receiving additional privileged information such as reference answers to enable self-evolution. This paper demonstrates that learning signals solely derived from the privileged teacher result in severe information leakage and unstable long-term training. Accordingly, we identify the optimal niche for self-distillation and propose RLSD (RLVR with Self-Distillation). Specifically, we leverage self-distillation to obtain token-level policy differences for determining fine-grained update magnitudes, while continuing to use RLVR to derive reliable update directions from environmental feedback (e.g., response correctness). This enables RLSD to simultaneously harness the strengths of both RLVR and OPSD, achieving a higher convergence ceiling and superior training stability.

Diffusion large language models (dLLMs) generate text by iteratively denoising a masked sequence, offering a parallel alternative to autoregressive models, but eliciting strong reasoning through post-training remains difficult: supervised fine-tuning is off-policy and suffers from exposure bias, while reinforcement learning gives only sparse, sequence-level rewards and is hard to apply without tractable sequence likelihoods. On-policy self-distillation (OPSD) offers a promising alternative, using one model as both student and teacher to provide dense, token-level, on-policy supervision, but its effectiveness hinges on giving the teacher privileged information (PI) - typically an instance-specific ground-truth reference unavailable at inference - so the student ends up distilling a weak PI-free consensus policy that yields little improvement on dLLM reasoning. We introduce dOPSD, which instead derives the teacher's privilege directly from the student's own denoising trajectory, evaluating masked positions using later, more-decoded steps of that same trajectory rather than an external label, so the teacher's advantage emerges from the model's own decoding process; on Dream and LLaDA, dOPSD improves both in-domain math reasoning and out-of-domain code generation, outperforming supervised and on-policy baselines.

Reinforcement learning (RL) has been widely used to train LLM agents for multi-turn interactive tasks, but its sample efficiency is severely limited by sparse rewards and long horizons. On-policy self-distillation (OPSD) alleviates this by providing dense token-level supervision from a privileged teacher that has access to ground-truth answers. However, such fixed privileged information cannot capture the diverse valid strategies in agent tasks, and naively combining OPSD with RL often leads to training collapse. To address these limitations, we introduce Skill-SD, a framework that turns the agent's own trajectories into dynamic training-only supervision. Completed trajectories are summarized into compact natural language skills that describe successful behaviors, mistakes, and workflows. These skills serve as dynamic privileged information conditioning only the teacher, while the student always acts under the plain task prompt and learns to internalize the guidance through distillation. To stabilize the training, we derive an importance-weighted reverse-KL loss to provide gradient-correct token-level distillation, and dynamically synchronize the teacher with the improving student. Experimental results on agentic benchmarks demonstrate that Skill-SD substantially outperforms the standard RL baseline, improving both vanilla GRPO (+14.0%/+10.9% on AppWorld/Sokoban) and vanilla OPD (+42.1%/+40.6%). Project page: https://k1xe.github.io/skill-sd/

On-policy knowledge distillation has proven effective for language models, yet its application to vision-language models (VLMs) remains underexplored. We observe that standard on-policy distillation can improve a student's output quality while failing to strengthen its reliance on visual input: on vision-critical tokens, the student's predictions remain largely unchanged whether or not fine-grained visual detail is present, even though the teacher's predictions depend heavily on it.To make this difference observable, we introduce visual advantage (VA), the token-level log-probability difference when the teacher scores a student-generated rollout with versus without access to fine-grained visual detail. VA is concentrated in a small minority of tokens, and these high-VA tokens are the ones that actually carry the visual supervision signal. This motivates a distillation objective that treats them differently from language scaffolding, so their contribution is not diluted by the abundant surrounding language tokens.We propose Visual-Advantage On-Policy Distillation (VA-OPD), which uses VA at two granularities: rollout-level reweighting by trajectory-averaged VA, and token-level KL averaged within high-VA and low-VA groups separately. We train on two math datasets (Geometry3K and ViRL39K) and evaluate on eight benchmarks covering both mathematical reasoning and visual understanding, across three teacher sizes (4B, 8B, and 32B) on the Qwen3-VL family. VA-OPD improves over standard on-policy distillation on every benchmark, with the gain growing monotonically along both the teacher-size and data-scale axes, suggesting that these factors compound consistently.

On-policy self-distillation (OPSD) is an emerging LLM post-training paradigm in which the model serves as its own teacher: conditioned on privileged information such as a reference trace or hint, the same policy provides dense token-level supervision on its own rollouts. However, recent studies show that OPSD degrades complex reasoning by suppressing predictive uncertainty, which supports exploration and hypothesis revision. Our token-level analysis shows that this failure arises from applying a uniform direction of teacher supervision across tokens with different uncertainty levels: conformity to the privileged self-teacher suppresses exploration at high entropy, while deviation from the teacher degrades step accuracy at low entropy. Accordingly, we propose Direction-Adaptive Self-Distillation (DASD), which reframes privileged self-distillation from uniform teacher imitation into entropy-routed directional supervision: high-entropy tokens are pushed away from the privileged teacher to preserve exploration, while low-entropy tokens are pulled toward the teacher to stabilize step-level execution. Across six mathematical reasoning benchmarks, DASD achieves the best macro Avg@16 over strong RLVR and self-distillation baselines. Pass@k, reasoning-health, and generalization analyses show that these average gains come from preserving exploration without sacrificing step-level execution.

On-policy (Self-)Distillation (OPD / OPSD) has shown strong potential for post-training large language models (LLMs). However, existing methods still rely heavily on external supervision, including ground-truth signals, environmental feedback, or guidance from larger models, and therefore fall short of genuine "self"-distillation. In this study, we show that on-policy self-distillation can be achieved using only a model's own generations via internal consistency. We propose unsupervised on-policy self-distillation (U-OPSD). U-OPSD first samples multiple rollouts and constructs a pseudo solution by majority vote under a self-consistency threshold. It then conditions the model's distribution on the pseudo-solution and distills itself on the disagreeing completions, allowing the model to correct itself precisely where it is confidently wrong. Across diverse benchmarks, base models, and training settings, U-OPSD consistently improves over the base models and matches or surpasses supervised methods with ground truth (GT) such as OPSD and GRPO. On five mathematical reasoning benchmarks, i.e., AIME24, AIME25, HMMT25, MATH500, and AMC23, U-OPSD improves over the base model by 8.5% and 10.7% on Qwen3 non-thinking mode at 4B and 8B scales, and outperforms OPSD by 3.2% and 2.3% on average, respectively. In thinking mode, U-OPSD stays on par with OPSD, ahead by 0.9% at 4B and level at 8B and surpassing GRPO by 0.7% and 1.1%, respectively. Code is available at [https://github.com/williamium3000/u-opsd](https://github.com/williamium3000/u-opsd).

Text-Image-to-Video (TI2V) models are an emerging unified architecture, where a single model simultaneously supports text-to-video (T2V) and image-to-video (I2V) generation. Given a high-quality first frame or a detailed textual prompt, TI2V models unlock substantially better visual quality than their T2V mode, raising a natural question: can the capability elicited by such privileged conditions be internalized into the model's own base generation ability? A common approach toward this goal is model self-distillation. However, the most straightforward solution, supervised fine-tuning, follows an off-policy strategy: its supervision is confined to teacher-generated endpoints from a fixed offline distribution rather than student-visited states, lacking precise correction tailored to the evolving policy. Recent on-policy distillation methods instead suffer from condition-state mismatch, where supervision is steered toward the given first frame instead of the student's actual content, misleading the correction. To achieve self-distillation that absorbs the teacher's privileged prior while retaining precise policy correction, in this work, we propose Hybrid-Policy Self-Distillation (HPSD), a novel self-distillation framework where a single TI2V model acts as both teacher and student under different conditions: the teacher operates in TI2V mode with a high-quality first frame and an enhanced prompt, while the student runs in the base T2V mode with only the vanilla prompt. Specifically, the student inherits off-policy teacher trajectory points as anchors, locally refines them toward its own policy, and finally receives velocity-level supervision on these self-generated roll-outs. Extensive experiments demonstrate that HPSD significantly improves T2V performance while also delivering notable TI2V gains, effectively strengthening the model's base generation ability.

On-policy self-distillation (OPSD) is a promising approach to improve reasoning language models, but it remains brittle in practice: making it work reliably often requires substantial engineering effort. We identify a structural source of this difficulty: vanilla OPSD is precisely the β=1 member of a broader policy-optimization family, where β weights the KL penalty anchoring the student to a reference policy. This equivalence turns β from an implicit value fixed at one into a controllable regularization parameter, yielding a more general formulation that trades off proximity to a reference policy against privileged teacher guidance. We introduce β-OPSD and derive its optimal policy as a geometric interpolation between the reference policy and the privileged teacher. Directly optimizing this objective with reinforcement learning, however, would be costly and high-variance. Rather than optimize the RL objective directly, we turn its closed-form solution into a distillation target. Each value of β selects a target along the reference-to-teacher path, which we implement efficiently by mixing their token-level logits. In this way, inexpensive distillation approximates the solution of expensive policy optimization. Return-to-go credit assignment further aligns token updates with the sequence-level objective while retaining the simplicity of OPSD. Experiments on mathematical reasoning benchmarks show that β-OPSD consistently outperforms vanilla OPSD, improving optimization stability and downstream reasoning performance. Our results provide a principled route from self-distillation to policy optimization and back without sacrificing the efficiency that makes OPSD practical.

Knowledge distillation has become a primary mechanism for transferring reasoning and domain expertise from frontier Large Language Models (LLMs) to smaller, deployable students. However, the dominant paradigm remains off-policy: students train on static teacher-generated data and never encounter their own errors during learning. This train--test mismatch, an instance of exposure bias, causes prediction errors to compound autoregressively at inference time. On-Policy Distillation (OPD) addresses this by letting the student generate its own trajectories and receive teacher feedback on these self-generated outputs, grounding distillation in the theory of interactive imitation learning. Despite rapid growth spanning divergence minimization, reward-guided learning, and self-play, the OPD literature remains fragmented with no unified treatment. This survey provides the first comprehensive overview of OPD for LLMs. We introduce a unified f-divergence framework over on-policy samples and organize the landscape along three orthogonal dimensions: feedback signal (logit-based, outcome-based, or self-play), teacher access (white-box, black-box, or teacher-free), and loss granularity (token-level, sequence-level, or hybrid). We systematically analyze representative methods, examine industrial deployments, and identify open problems including distillation scaling laws, uncertainty-aware feedback, and agent-level distillation.

Large language model agents have shown strong potential in complex interactive tasks, yet their reinforcement learning (RL) is often hindered by sparse rewards, as a long multi-turn trajectory may receive only a single outcome-level signal. On-policy self-distillation (OPSD) provides dense token-level supervision from a privileged teacher, but the teacher may not be reliable at every position. Existing methods commonly rely on isolated token-level discrepancies, which can be sensitive to noise, or assign a shared step-level weight that may overlook positional variation. We propose Persistent Consistency Self-Distillation (PCSD), which derives token-level distillation weights from the local persistence of teacher-favoring signals. PCSD combines adaptive windows with exponentially decayed aggregation to capture persistent relative teacher support, applies trend-aware modulation to attenuate locally declining support, and produces continuous weights through sigmoid gating. The resulting objective is jointly optimized with GRPO, combining dense teacher guidance with sparse environmental feedback. Without inference-time skills, PCSD achieves the best ALFWorld Overall results among all baselines on both backbones, exceeding GRPO by 15.6 and 13.3 points and SDAR by 6.2 and 5.5 points, while remaining competitive on WebShop and gaining 15.8 points over GRPO on unseen ALFWorld split.

Reinforcement learning can align diffusion models with human preferences and task-specific objectives, but endpoint rewards do not specify how an intermediate denoising prediction should change. We introduce DiffusionOPSD as an on-policy self-distillation framework that converts image-level reward guidance into explicit targets for clean-output predictions at sampled queries. At each outer iteration, a frozen behavior policy generates trajectories and supplies query states and anchors. Reward gradients construct bounded positive and negative targets around each anchor. The trainable policy fits these targets as detached supervision through finite fitting before an exponential moving average update refreshes the behavior policy. This setup lets us measure target construction and finite realization separately. Controlled same-query experiments show that larger target-construction gains do not necessarily translate into larger realized gains after a single fitting update. Across SD 3.5-M and the step-distilled Z-Image-Turbo, our approach achieves the best final held-out scores in 19 of 20 reward-matched settings across two backbones and ten evaluators. It outperforms the strongest competing method by up to 44.0% and reduces training GPU-hours relative to DiffusionNFT by 40% on SD 3.5-M and 63% on Z-Image-Turbo. These results support on-policy self-distillation as an efficient and analyzable approach to diffusion post-training by converting image-level reward guidance into explicit and continually refreshed intermediate supervision, thereby opening a path toward more efficient and diagnosable alignment.

The landscape of high-performance image generation models is currently shifting from the inefficient multi-step ones to the efficient few-step counterparts (e.g, Z-Image-Turbo and FLUX.2-klein). However, these models present significant challenges for directly continuous supervised fine-tuning. For example, applying the commonly used fine-tuning technique would compromises their inherent few-step inference capability. To address this, we propose D-OPSD, a novel training paradigm for step-distilled diffusion models that enables on-policy learning during supervised fine-tuning. We first find that the modern diffusion model where the LLM/VLM serves as the encoder can inherit its encoder's in-context capabilities. This enables us to make the training as an on-policy self-distillation process. Specifically, during training, we make the model acts as both the teacher and the student with different contexts, where the student is conditioned only on the text feature, while the teacher is conditioned on the multimodal feature of both the text prompt and the target image. Training minimizes the two predicted distributions over the student's own roll-outs. By optimized on the model's own trajectory and under it's own supervision, D-OPSD enables the model to learn new concept, style, etc. without sacrificing the original few-step capacity.

On-policy self-distillation (OPSD) provides dense, token-level supervision for reasoning models by aligning a model's own distribution with the distribution it produces under privileged context, typically a verified solution. However, we show that the learning signal drawn from this distributional gap concentrates on style tokens rather than task-bearing ones, as the hinted model tends to produce more direct, shorter outputs. We term this pathology privilege-induced style drift, which destabilizes training or causes response length to shrink. To address this, we propose RLCSD (Reinforcement Learning with Contrastive on-policy Self-Distillation), which mitigates this drift by contrasting the teacher-student gap under a correct hint against that under a wrong hint, suppressing the style shift that conditioning on a hint tends to induce regardless of correctness, and yielding a signal that is more concentrated on task-bearing tokens. Experiments on Qwen3 (1.7B/4B/8B) and Olmo-3-7B-Think across mathematical and logical reasoning show that RLCSD consistently outperforms GRPO and prior OPSD methods. We further show that the contrastive principle is general: it plugs into existing OPSD methods to improve them, and its underlying insight extends to the broader cross-model on-policy distillation setting.

Graphical user interface (GUI) grounding requires vision-language models (VLMs) to identify small target elements in high-resolution screenshots and predict precise screen coordinates. On-policy self-distillation (OPSD) is a promising post-training approach for this coordinate-sensitive task, since it provides dense token-level teacher signals beyond hard coordinate labels. However, naive OPSD is not well suited to GUI grounding: OPSD evaluates the teacher on student-generated prefixes, the quality of coordinate-token teacher signals can degrade when the prefix has already deviated from the target coordinate, leading to unreliable teacher signal. To mitigate this, We propose quality-aware self-distillation for VLM-based GUI grounding, which improves coordinate-token teacher-signal quality through soft correctness-aware gating and teacher-probability scaling. The soft correctness-aware gate checks whether the teacher's current coordinate-token prediction can still be completed into the ground-truth box under the student-generated prefix. If not, the corresponding teacher signal is down-weighted. Teacher-probability scaling then uses the teacher's confidence as a lightweight factor to further calibrate the strength of the gated supervision. A key empirical finding is that neither component alone improves overall performance, whereas combining them consistently improves performance. This suggests that the two mechanisms play complementary roles: correctness-aware gating suppresses unreliable coordinate-token supervision, while teacher-probability scaling calibrates the strength of the remaining signals. Experiments across six GUI grounding benchmarks show that our method consistently improves the base model and outperforms strong baselines.

Self-distillation enables language models to learn on-policy from their own trajectories by using the same model as both student and teacher, with the teacher being conditioned on privileged information unavailable to the student. Such information can come in different types or views, such as solutions, demonstrations, feedback, or final answers. This setup provides dense token-level feedback without relying on a separate external model, but creates a fundamental asymmetry: the teacher may rely on view-specific information that the student cannot access at inference time. Moreover, the best type of privileged information is often task-dependent, making it difficult to choose a single teacher view. In this work, we address both these challenges jointly by introducing AVSD (Adaptive-View Self-Distillation), a novel method of self-distillation with multiple privileged-information views, which reconstructs token-level supervision by separating stable cross-view consensus from view-specific residual signals. AVSD identifies the consensus signal shared across views, which provides a reliable update direction, and then selectively adds the view-specific residual signal to adjust the update magnitude when it both aligns with the consensus direction and remains proportionate to the consensus signal. Experiments on math competition benchmarks (AIME24, AIME25, and HMMT25) show that AVSD consistently outperforms both single-view self-distillation baselines and GRPO, achieving average Avg@8 gains of 3.1% and 2.2% over the strongest baselines on Qwen3-8B and Qwen3-4B, respectively. Moreover, on code-generation benchmarks (Codeforces, LiveCodeBench v6) using Qwen3-8B, AVSD outperforms the single-view self-distillation baseline by 2.4% on average.

On-policy self-distillation (OPSD) has proven effective for post-training large language models (LLMs), yet its application to diffusion LLMs (dLLMs) remains unexplored. Existing OPSD methods are inherently autoregressive-centric. They inject privileged information via left-to-right prefix conditioning with token-level divergence supervision, a design that fundamentally conflicts with the arbitraryorder generation of dLLMs. We introduce d-OPSD, the first OPSD framework tailored for dLLMs. Our approach makes two core contributions. First, we reframe self-teacher construction by using self-generated answers as suffix conditioning, enabling the student model to learn from "self future-experience" rather than privileged prefixes. Second, we shift supervision from token-level to step-level, aligning training with the iterative denoising process of dLLMs. Experiments across four reasoning benchmarks show that d-OPSD consistently outperforms RLVR and SFT baselines with superior sample efficiency, requiring only around 10% of the optimization steps by RLVR and opening a promising pathway for dLLM posttraining. The code is available at https://github.com/xingzhejun/d-OPSD.

Reinforcement learning with verifiable rewards (RLVR) has substantially improved the reasoning capabilities of large language models on tasks such as mathematical reasoning and code generation. However, most RLVR methods assign a scalar outcome reward to an entire trajectory, resulting in sparse supervision and limited token-level credit assignment. On-policy distillation (OPD) provides denser supervision by distilling token-level distributions from a stronger teacher model, but requires an additional teacher and typically assumes a shared vocabulary. On-policy self-distillation (OPSD) removes this dependency by conditioning the same model on privileged information to construct a teacher policy. However, directly matching the teacher distribution may cause information leakage and unstable optimization. RLSD avoids direct matching by using the teacher signal only to modulate update magnitudes, but it cannot provide an explicit correction direction when the sampled reasoning fails. To address this tradeoff, we introduce H^{2}SD, a hybrid hindsight self distillation framework that uses the teacher differently according to trajectory correctness. For successful trajectories, the teacher receives the student response confirmed as correct together with a rephrasing instruction, and its probabilities on the original response tokens are used to modulate update magnitudes without changing the direction determined by the reward. For failed trajectories, we condition the teacher on a reference hint containing key reasoning steps and a verified answer, and minimize the reverse KL divergence from the student to the teacher. Experiments on multiple challenging reasoning benchmarks show that H^2SD consistently outperforms representative RLVR, OPSD, and RLSD baselines while maintaining stable optimization and favorable generation efficiency.

Enabling agents to learn from experience and internalize it into their policy has become a central problem in self-evolving AI. On-policy self-distillation (OPSD) offers an effective pathway by using a privileged self-teacher to provide dense supervision on the student's own trajectories; however, existing methods still rely heavily on designer-specified privileged artifacts (e.g., answers, feedback, skills, or trajectories), limiting the end-to-end learnability and scalability required for continual self-improvement. In this work, we introduce Latent On-Policy Self-Distillation (LOPD), which, rather than proposing another hand-crafted OPSD variant with a newly prescribed form of privileged context, makes the teacher's privileged context itself learnable end-to-end from experience. Technically, LOPD retrieves relevant experiences and composes them into continuous latent tokens that condition a self-teacher, while the student generates trajectories from the task and interaction history and receives dense token-level supervision at every visited prefix. We further introduce a privileged-margin objective to stabilize and regulate the learning of latent context. Empirically, LOPD demonstrates (I) strong performance, outperforming RLVR and representative OPSD methods including OPSD, SDPO, and Skill-SD across both agentic tool use and code generation; and (II) high learning efficiency, surpassing GRPO and Skill-SD with less than 30% of their rollout budget. Ablation studies further provide direct evidence that making privileged context learnable is necessary for realizing these gains. Together, these results position LOPD as a step toward a more scalable and self-directed paradigm for agent evolution.

Deep search agents operate over trajectories spanning dozens of steps, yet standard reinforcement learning provides only a single outcome reward per trajectory, which is far too sparse for effective credit assignment. On-policy self-distillation (OPSD) addresses this by using the model's own logits as dense token-level teachers, but extending it to search agents introduces a fundamental tension: the teacher, having access to privileged information such as the correct answer, produces a distribution that differs systematically from the student's exploration-based reasoning, and naive distillation causes the student to inherit this information asymmetry rather than learn better search strategies. We resolve this tension through two contributions. First, we construct Evidence Anchors, which are concise, step-level evidence snippets extracted from the web, as privileged information that captures key reasoning steps without revealing the entire answer path. Second, we propose Step-Level Self-Distilled Policy Optimization (SSPO), which converts teacher-student disagreement into step-level advantage weights within GRPO, applied exclusively to incorrect trajectories. This design decouples what to update from how much to update: the outcome reward determines the direction of policy change, while the teacher modulates its magnitude at each step. Correct trajectories are left untouched, preserving their diversity. On Qwen3-8B, SSPO consistently outperforms GRPO across BrowseComp, GAIA, and FRAMES, surpassing or matching GRPO trained with twice as many gradient steps while adding only about 5 percent overhead per step from a single additional forward pass.

Reinforcement learning (RL) has emerged as a central paradigm for post-training LLM agents, yet its trajectory-level reward signal provides only coarse supervision for long-horizon interaction. On-Policy Self-Distillation (OPSD) complements RL by introducing dense token-level guidance from a teacher branch augmented with privileged context. However, transferring OPSD to multi-turn agents proves problematic: compounding multi-turn instability destabilizes supervision, while skill-conditioned privileged guidance requires asymmetric treatment for negative teacher rejections may arise from imperfect skills retrieval or utilization. We introduce SDAR (Self-Distilled Agentic Reinforcement Learning), which treats OPSD as a gated auxiliary objective while keeping RL as the primary optimization backbone. SDAR maps detached token-level signals into a sigmoid gate, strengthening distillation on teacher-endorsed positive-gap tokens and softly attenuating negative teacher rejections. Across the Qwen2.5 and Qwen3 families on ALFWorld, WebShop, and Search-QA, SDAR substantially improves over GRPO (+9.4% on ALFWorld, +7.0% on Search-QA, +10.2% on WebShop-Acc), avoids the instability of naive GRPO+OPSD, and consistently outperforms hybrid RL--OPSD baselines across model scales.

Multimodal on-policy distillation (OPD) transfers fine-grained visual knowledge by supervising student-generated trajectories with a privileged-view teacher. Yet its next-token corrections are source-mixed, combining visual signals with linguistic priors and teacher-specific effects. The key challenge is to estimate which corrections are supported by visual evidence, not merely where or how strongly to distill. We introduce Visual Attribution Distillation (VAD), a counterfactual target-reconstruction algorithm that estimates the visually attributable part of a teacher correction. At each student-generated prefix, VAD evaluates the same fixed teacher with the relevant evidence present and removed. The corresponding change in centered log-probabilities defines ut, a signed proxy for the visual evidence direction that estimates how revealing the evidence supports or refutes candidate tokens. VAD projects the original correction onto this proxy to obtain an intervention-aligned component and a proxy-unexplained residual, then reconstructs a student-anchored target from the former. During training, this reconstructed target supplies the primary supervision signal, while the privileged teacher contributes a weak regularizer. Across six fine-grained visual benchmarks at 4B and 9B scales, VAD outperforms direct privileged-view distillation and visual-advantage weighting. Token- level and controlled-target analyses show that the proxy-aligned component is enriched in task-relevant visual corrections and yields stronger target shifts, especially when evidence refutes a mistaken answer. These results support counterfactual target reconstruction as an effective alternative to source-mixed supervision.

Continual post-training enables foundation models to acquire new knowledge while preserving existing capabilities. Recent work suggests that on-policy learning can mitigate forgetting, with on-policy self-distillation emerging as a particularly attractive approach. In this work, we revisit this optimistic view through self-distillation policy optimization (SDPO). Our experiments show that SDPO can accelerate in-domain specialization when teacher signals are stable and well aligned, but it struggles to generalize to out-of-distribution scenarios. In continual post-training, SDPO exhibits stronger forgetting and can even collapse, whereas on-policy reinforcement learning methods such as GRPO adapt more conservatively and better preserve prior capabilities. Further analyses reveal that denser self-distillation induces larger drift in both parameter space and response space, and can amplify high-frequency formatting artifacts through a self-reinforcing teacher--student loop. These findings suggest that on-policy data alone is insufficient for continual learning. Dense self-distillation can accelerate specialization when teacher targets are stable and token-level supervision is reliable, but it should not be treated as a default stabilizer for continual post-training. Our code is available at https://github.com/Moenupa/SDPO-CL.

On-policy distillation is pivotal for transferring reasoning capabilities to capacity-constrained models, yet remains prone to instability and negative transfer. We show that on-policy distillation can be interpreted, both theoretically and empirically, as a form of policy optimization, where the teacher-student log-likelihood ratio acts as a token reward. From this insight, we introduce REOPOLD (Relaxed On-Policy Distillation) a framework that stabilizes optimization by relaxing the strict imitation constraints of standard on-policy distillation. Specifically, REOPOLD temperately and selectively leverages rewards from the teacher through mixture-based reward clipping, entropy-based token-level dynamic sampling, and a unified exploration-to-refinement training strategy. Empirically, REOPOLD surpasses its baselines with superior sample efficiency during training and enhanced test-time scaling at inference, across mathematical, visual, and agentic tool-use reasoning tasks. Specifically, REOPOLD outperforms recent RL approaches achieving 6.7~12x greater sample efficiency and enables a 7B student to match a 32B teacher in visual reasoning with a ~3.32x inference speedup.

On-Policy Self-Distillation (OPSD) has emerged as a popular paradigm for large language model (LLM) self-improvement, allowing models to act as their own teachers by leveraging privileged information such as ground-truth solutions. However, recent findings indicate that OPSD can severely degrade the performance of LLMs on complex reasoning tasks: By forcing the student to imitate an artificially confident reasoning trace conditioned on privileged information, OPSD inadvertently suppresses expressions of uncertainty and penalizes the exploratory, self-corrective behaviors required to solve challenging problems. To address this, we introduce Negative Self-Distillation (NSD), a new framework that optimizes LLMs by diverging from flawed reasoning rather than imitating privileged solutions. Instead of relying on ground-truth answers or external supervision, NSD uses the model itself to generate a question-specific negative condition (eg, acting as a ``careless reasoner'') and pushes the student's distribution away from this self-generated negative teacher. Naively applying unlearning objectives to achieve this divergence is problematic, as flawed reasoning tokens are confounded with basic linguistic tokens; indiscriminately penalizing both risks catastrophically degrading the model's foundational language capabilities. We resolve this by designing a dynamic gating mechanism that automatically identifies and isolates reasoning-critical tokens, ensuring gradient updates target only behavioral flaws while preserving the model's linguistic priors. Empirically, NSD consistently outperforms OPSD and other label-free, self-bootstrapping reinforcement learning (RL) baselines.

On-policy Distillation (OPD) supervises a student model on trajectories sampled from its own policy by minimizing the divergence between the output distributions of the teacher and student at each token position, thereby providing dense token-level supervision. Although existing OPD methods have demonstrated strong performance in improving the reasoning ability of student models, their objectives fundamentally rely on token-level distribution matching. Consequently, they lack an explicit signal for comparing a token's relative compatibility across reasoning modes and thus do not directly model preferences between these modes. To address this limitation, we propose COPD, a contrastive OPD framework. Specifically, for each token generated by the student model, a frozen teacher model scores the same student state under two contrasting instructions that elicit light and heavy reasoning. The difference between the resulting log probabilities serves as a token-level advantage signal to guide the OPD update. Rather than merely imitating a single teacher distribution, COPD directly encourages the student model to learn more concise and efficient reasoning strategies. We conduct experiments on nine multimodal benchmarks covering both reasoning and understanding tasks. The results show that COPD substantially reduces reasoning length without compromising model performance and consistently improves efficiency across different tasks and model scales. Furthermore, the contrastive formulation can be seamlessly integrated into the On-policy Self-distillation (OPSD) framework, where self-contrastive supervision is constructed without an additional teacher model, thereby enabling the model to distill itself toward lightweight reasoning.

Outcome-based reinforcement learning provides a stable optimization backbone for language agents, but its sparse trajectory-level rewards provide little guidance on which intermediate decisions should be reinforced or suppressed. On-policy self-distillation offers dense token-level supervision, yet existing skill-conditioned variants often rely on external skill memories or retrieved privileged context, which are costly to maintain and can be mismatched with the state distribution induced by the current policy in multi-turn interaction. We propose OPID (On-Policy Skill Distillation), a framework that extracts skill supervision directly from completed on-policy trajectories. OPID represents trajectory hindsight as hierarchical skills: episode-level skills capture global workflows or failure-avoidance rules, while step-level skills capture local decision knowledge at critical timesteps. A critical-first routing mechanism uses step-level skills when critical decisions are identified and falls back to episode-level skills as default guidance otherwise. The selected skill is injected into the interaction history, allowing the old policy to re-score the same sampled response under both original and skill-augmented contexts. The resulting log-probability shift yields a token-level self-distillation advantage, which is combined with the outcome advantage for policy optimization. OPID thus preserves RL as the primary training objective while introducing dense, distribution-matched hindsight supervision. Experiments on ALFWorld, WebShop and Search-based QA demonstrate that OPID generally improves agent performance, sample efficiency, and robustness over outcome-only RL and existing skill-distillation baselines. Our code is available at https://github.com/jinyangwu/OPID/tree/main.

Reinforcement learning from verifiable rewards (RLVR) suffers from sparse outcome signals, creating severe exploration bottlenecks on complex reasoning tasks. Recent on-policy self-distillation methods attempt to address this by utilizing language feedback to generate dense, token-level supervision. However, these approaches rely on a fixed, passive teacher to interpret the feedback. As the student policy improves, the teacher's zero-shot assessment capabilities plateau, ultimately halting further learning. To overcome this, we propose Variational Policy Distillation (VPD), a framework that formalizes learning from language feedback as a Variational Expectation-Maximization (EM) problem. VPD co-evolves both policies: in the E-step, the teacher is actively refined on trajectory outcomes via an adaptive trust-region update, translating textual feedback into a dynamically improved target token distribution. In the M-step, the student internalizes this dense distributional guidance on its own on-policy rollouts. By continuously improving the teacher's ability to extract actionable signals from textual critique, VPD overcomes the limitations of passive distillation. Evaluated across diverse sources of diagnostic feedback on scientific reasoning and code generation tasks, VPD consistently outperforms both standard RLVR and existing self-distillation baselines. Finally, by stress-testing our framework on rigid mathematical reasoning and cold-start regimes, we illuminate the fundamental bounds of feedback-driven self-distillation compared to pure environment-driven RL.

On-policy self-distillation (self-OPD) densifies reinforcement learning with verifiable rewards (RLVR) by letting a policy teach itself under privileged context. We find that when this guidance spans the full response, all-token KL spends gradients on mostly redundant positions and amplifies privileged-information leakage, causing entropy rise, shortened reasoning, and out-of-distribution degradation in long-horizon math training. We propose Token-Routed Alignment for Critical rEasoning (TRACE), which distills only on annotator-marked critical spans: forward KL on key spans of correct rollouts, optional reverse KL on localized error spans, and GRPO on all remaining tokens, with the KL channel annealed away after a short warm-up. Our analysis explains TRACE through two effects: forward KL provides non-vanishing lift to teacher-supported tokens that the student under-allocates, while span masking and decay keep cumulative privileged-gradient exposure finite. On four held-out math benchmarks plus GPQA-Diamond, TRACE improves over GRPO by 2.76 percentage points on average and preserves the Qwen3-8B base OOD score on GPQA-Diamond, where GRPO and all-token self-OPD baselines degrade. Gains persist under online self-annotation (+1.90 percentage points, about 69% of the strong-API gain), reducing the concern that TRACE merely imports external annotator capability. Across scales, the best routed action is base-dependent: on Qwen3-8B it is forward KL on key spans, while on Qwen3-1.7B it shifts to reverse KL on error spans.

On-policy distillation (OPD) and on-policy self-distillation (OPSD) have emerged as promising post-training methods for large language models, offering dense token-level supervision on trajectories sampled from the model's own policy. However, existing results on their effectiveness remain mixed: while OP(S)D has shown promise in system prompt and knowledge internalization, recent studies also report instability and degradation. In this work, we present a comprehensive empirical study of when OPD and OPSD work, when they fail, and why. We find that OPD on mathematical reasoning is highly sensitive to teacher choice and loss formulation, whereas OPSD fails in our tested settings due to test-time absence of instance-specific privileged information (PI). In contrast, OPSD is effective when PI represents a shared latent rule, such as a system prompt or alignment preference. We identify three failure mechanisms: (1) distribution mismatch between teacher and student caused by conditioning on student-generated prefixes, (2) optimization instability from biased TopK reverse-KL gradients, and (3) an OPSD-specific limitation where the student learns a PI-free policy that aggregates PI-conditioned teachers, which is insufficient when PI is instance-specific. We further show that stop-gradient TopK objectives, RLVR-adapted teachers, and SFT-stabilized students mitigate these failures.

Knowledge distillation improves large language model (LLM) reasoning by compressing the knowledge of a teacher LLM to train smaller LLMs. On-policy distillation advances this approach by having the student sample its own trajectories while a teacher LLM provides dense token-level supervision, addressing the distribution mismatch between training and inference in off-policy distillation methods. However, on-policy distillation typically requires a separate, often larger, teacher LLM and does not explicitly leverage ground-truth solutions available in reasoning datasets. Inspired by the intuition that a sufficiently capable LLM can rationalize external privileged reasoning traces and teach its weaker self (i.e., the version without access to privileged information), we introduce On-Policy Self-Distillation (OPSD), a framework where a single model acts as both teacher and student by conditioning on different contexts. The teacher policy conditions on privileged information (e.g., verified reasoning traces) while the student policy sees only the question; training minimizes the per-token divergence between these distributions over the student's own rollouts. We demonstrate the efficacy of our method on multiple mathematical reasoning benchmarks, achieving 4-8x token efficiency compared to reinforcement learning methods such as GRPO and superior performance over off-policy distillation methods.

On-policy distillation (OPD) trains a student on its own trajectories with dense per-token supervision from a stronger teacher, and often outperforms off-policy distillation and standard reinforcement learning. However, we find that its effectiveness implicitly relies on two assumptions that frequently break in practice: trajectory-level alignment between the student and the teacher, and uniform token-level reliability of the teacher's preferences. We therefore propose Sign-Gated On-Policy Distillation (SG-OPD), which uses a binary verifier as a trust signal for the teacher at two complementary granularities: phased teacher sampling mixes in verifier-endorsed teacher rollouts at cold-start, and a sign-consistency gate extrapolates the distillation update on tokens where the teacher agrees with the verifier-correct direction and interpolates it where it disagrees. Experiments on competition-level mathematical reasoning benchmarks show that SG-OPD consistently outperforms standard OPD, with average gains of 1.98 and 7.50 at the per-sample and per-question levels, respectively.

On-policy (self) distillation (OPSD) is increasingly adopted for language-model post-training. It strengthens the teacher with privileged information but can induce a privilege illusion: the student learns privilege-dependent behavior it cannot reproduce from its inference-time context, yet behaves as if the training-time privileged information remained available, ultimately degrading performance. In this paper, we identify information asymmetry between the privileged teacher and the student at inference as the root cause of this failure in OPSD. To resolve this asymmetry, we propose Dual-Anchored Policy Distillation (DAPD), a unified framework with two levels of anchoring. Dual-Path Anchoring (DPA) introduces a self-conditioned bridge and aligns reference and rollout behavior along two matched-information paths, preventing privilege-dependent behavior from being transferred to the inference-time student. Dual-Source Anchoring (DSA) applies these paths in both reference-to-rollout and rollout-to-reference directions, reducing reliance on privileged reference guidance while preserving correctness supervision. Extensive experiments show that DAPD significantly alleviates privilege illusion, outperforming OPSD on Qwen3-4B by +2.00 points on average across tasks. Notably, its gains persist across scales, reaching +2.69 at 4B and +2.78 at 32B.

On-policy distillation (OPD) trains a student on its own trajectories with token-level teacher feedback and often outperforms off-policy distillation and standard reinforcement learning. However, we find that its standard advantage weighted policy gradient suffers from three structural weaknesses, including high variance updates, vanishing gradients in zero-advantage regions, and exploration bottlenecks when corrective signals are insufficient. We therefore propose Asymmetric On-Policy Distillation (AOPD), which replaces ineffective negative reinforcement with localized divergence minimization in non-positive advantage regions while preserving positive reinforcement learning. Experiments on mathematical reasoning benchmarks show that AOPD consistently outperforms standard OPD, with average gains of 4.09 / 8.34 under strong / weak initialization, respectively. AOPD also maintains higher policy entropy during training and better capability retention during sequential tool-use adaptation.

On-Policy Self-Distillation (OPSD) has recently emerged as an alternative to Reinforcement Learning with Verifiable Rewards (RLVR), promising higher accuracy and shorter responses through token-level credit assignment from a self-teacher conditioned on privileged context. However, this promise does not carry over to thinking-enabled mathematical reasoning, where reported accuracy gains shrink and sometimes turn negative. We hypothesize that hindsight supervision can specify better token-level alternatives in short thinking-disabled outputs, but in long thinking-enabled traces it more readily identifies redundancy than supplies better replacements. To test this, we applied OPSD separately to correct and incorrect rollout groups, so that compression and correction can be observed in isolation. Our results show that in thinking-enabled mathematical reasoning, OPSD behaves most reliably as a compression mechanism rather than a correction mechanism: training only on correct rollouts preserves accuracy while substantially shortening responses, whereas training only on incorrect rollouts damages accuracy. In light of these findings, we propose a revised post-training pipeline for thinking-enabled mathematical reasoning: SFT then RLVR then OPSD.

On-policy distillation (OPD) has recently emerged as an effective post-training paradigm for consolidating the capabilities of specialized expert models into a single student model. Despite its empirical success, the conditions under which OPD yields reliable improvement remain poorly understood. In this work, we identify two fundamental bottlenecks that limit effective OPD: insufficient exploration of informative states and unreliable teacher supervision for student rollouts. Building on this insight, we propose Uni-OPD, a unified OPD framework that generalizes across Large Language Models (LLMs) and Multimodal Large Language Models (MLLMs), centered on a dual-perspective optimization strategy. Specifically, from the student's perspective, we adopt two data balancing strategies to promote exploration of informative student-generated states during training. From the teacher's perspective, we show that reliable supervision hinges on whether aggregated token-level guidance remains order-consistent with the outcome reward. To this end, we develop an outcome-guided margin calibration mechanism to restore order consistency between correct and incorrect trajectories. We conduct extensive experiments on 5 domains and 16 benchmarks covering diverse settings, including single-teacher and multi-teacher distillation across LLMs and MLLMs, strong-to-weak distillation, and cross-modal distillation. Our results verify the effectiveness and versatility of Uni-OPD and provide practical insights into reliable OPD.

Training-time privileged information (PI) can enable language models to succeed on tasks they would otherwise fail, making it a powerful tool for reinforcement learning in hard, long-horizon settings. However, transferring capabilities learned with PI to policies that must act without it at inference time remains a fundamental challenge. We study this problem in the context of distilling frontier models for multi-turn agentic environments, where closed-source systems typically hide their internal reasoning and expose only action trajectories. This breaks standard distillation pipelines, since successful behavior is observable but the reasoning process is not. For this, we introduce π-Distill, a joint teacher-student objective that trains a PI-conditioned teacher and an unconditioned student simultaneously using the same model. Additionally, we also introduce On-Policy Self-Distillation (OPSD), an alternative approach that trains using Reinforcement Learning (RL) with a reverse KL-penalty between the student and the PI-conditioned teacher. We show that both of these algorithms effectively distill frontier agents using action-only PI. Specifically we find that π-Distill and in some cases OPSD, outperform industry standard practices (Supervised finetuning followed by RL) that assume access to full Chain-of-Thought supervision across multiple agentic benchmarks, models, and forms of PI. We complement our results with extensive analysis that characterizes the factors enabling effective learning with PI, focusing primarily on π-Distill and characterizing when OPSD is competitive.

Multilingual reasoning transfer is crucial for extending reasoning capabilities of large language models (LLMs) beyond high-resource languages. On-policy self-distillation (OPSD) and its variants have emerged as a promising paradigm, providing dense token-level supervision on student-generated rollouts, yet their objectives do not explicitly prioritize reasoning signals most critical to cross-lingual transfer. We characterize that target-language reasoning comprises the generation of both surface text and reasoning pivots, which are decisions that advance or redirect the reasoning process and shape subsequent inference. This motivates concentrating privileged distillation around such pivots. We therefore propose RP-OPSD, Reasoning-Pivot-guided On-Policy Self-Distillation, using the distributional shift between matched teacher views with and without an English reference solution as an operational proxy to guide privileged distillation and reference anchoring. Experiments on mathematical reasoning benchmarks covering 17 languages and multiple difficulty levels show that our method outperforms strong multilingual reasoning baselines and OPSD variants. Further analysis reveals that RP-OPSD concentrates privileged distillation on reasoning-control and problem-condistioned state-update tokens, while downweighting it for tokens that mainly support surface realization. Our code is available at https://github.com/NJUNLP/RP-OPSD.

On-policy self-distillation, where a language model conditions on privileged context to supervise its own generations, is a promising source of dense supervision for sparse-reward reinforcement learning. Actually, it can be instantiated as an auxiliary full-vocabulary student-to-teacher reverse Kullback-Leibler divergence loss. We therefore propose SDPG, a self-distilled policy-gradient framework that combines group-relative verifier advantages with normalized standard deviation, exact full-vocabulary on-policy self-distillation, as well as reference-policy KL regularization. Empirically, SDPG improves stability and performance over RLVR and self-distillation baselines. The code is available at https://github.com/lauyikfung/SDPG.

Tool-Integrated Reasoning (TIR) enables LLMs to solve complex tasks through iterative tool interactions. However, existing reinforcement learning methods often rely on trajectory-level supervision, limiting fine-grained credit assignment in long-horizon TIR scenarios. On-policy self-distillation offers denser signals through teacher branches with privileged context, but existing approaches typically derive such context from ground-truth answers or retrieved skills, which may not reflect the states actually visited by the agent. Moreover, token-level supervision fails to capture the turn-level structure of tool interactions. To address this, we propose TurnSight, a turn-level hindsight self-distillation framework that derives supervision directly from execution-conditioned hindsight. It then constructs multiple hindsight views with different lookahead horizons and selects reliable supervision through cross-horizon directional agreement. Finally, the selected hindsight signal is normalized across sibling rollouts and used to adaptively modulate RL advantages while preserving their original optimization direction. Extensive experiments on three benchmarks demonstrate the effectiveness of TurnSight. Our codes are available at https://github.com/quchangle1/TurnSight.

On-policy self-distillation (OPSD) lets a language model learn from a frozen copy of itself that sees an answer or a worked solution. Giving the teacher this extra information seems to offer the student more to learn, but how much does it add beyond distillation itself? To isolate that contribution, we construct AMPLE-Math, a reusable suite of 5,319 mathematical problems with six reasoning views that share the same answer, and compare each view with matched reference-free distillation. With a thinking-enabled teacher supervising direct-response rollouts, reference-free distillation accounts for much of Qwen3-1.7B's improvement under thinking-enabled evaluation, both in domain and on external benchmarks. Evidence for an additional reference benefit is modest in Qwen, strongest for a polished solution, whereas complete traces add two percentage points in SmolLM3-3B at step 50. These benefits depend on the student being trained. At the same checkpoint, replacing short direct-response rollouts with long thinking-enabled rollouts turns gains into losses in both families while the problems, references, and evaluation stay fixed. Teacher profiles and matched loss interventions in Qwen further show that changing token-level supervision can leave student behavior largely unchanged. Together, these findings suggest that OPSD can improve access to existing reasoning capabilities through parameters shared by direct-response and thinking-enabled inference. The value of a privileged reference is what it adds to this cross-mode transfer, not how much of the solution it reveals.

Tool-integrated reasoning (TIR) is difficult to scale to small language models due to instability in long-horizon tool interactions and limited model capacity. While reinforcement learning methods like group relative policy optimization provide only sparse outcome-level rewards. Recently, on-policy distillation (OPD) has gained popularity by supplying dense token-level supervision from a teacher on student-generated trajectories. However, our experiments indicate that applying OPD to TIR leads to a critical failure mode: erroneous tool calls tend to cascade across subsequent reasoning steps, progressively amplifying student-teacher divergence and rendering the teacher's token-level supervision increasingly unreliable. To address this, we propose SOD, a step-wise on-policy distillation framework for small language model agents, which adaptively reweights distillation strength at each step based on step-level divergence. Therefore, SOD can attenuate potentially misleading teacher signals in high-divergence regions while preserving dense guidance in well-aligned states. Experiments on challenging math, science, and code benchmarks show that SOD achieves up to 20.86% improvement over the second-best baseline. Notably, our 0.6B student achieves 26.13% on AIME 2025, demonstrating effective transfer of agentic reasoning to lightweight models. Our code is available at https://github.com/YoungZ365/SOD.

On-policy distillation (OPD), which samples trajectories from the student model and supervises them with a teacher at the token level, avoids relying solely on verifiable terminal rewards and can yield better generalization than off-policy distillation. However, OPD requires expensive on-the-fly sampling of the student policy during training, which substantially increases training cost, especially for long responses. Our initial analysis shows that, during OPD, training signals are often concentrated in the prefix of each output, and that even a short teacher-generated prefix can significantly help the student produce the correct answer. Motivated by these observations, we propose a simple yet effective modification of OPD: we apply the distillation objective only to prefixes of student-generated outputs and terminate each sampling early during distillation. Experiments on a suite of AI-for-Math and out-of-domain benchmarks show that on-policy prefix distillation matches the performance of full OPD while reducing training FLOP by 2x-47x.

On-policy self-distillation (OPSD) trains a student on its own rollouts using a privileged teacher, but its standard objective weights all generated tokens equally, implicitly treating the privileged teacher target as equally reliable at every student-visited prefix. Existing entropy-based OPD methods relax this uniformity by modulating token-level supervision with teacher entropy, but high teacher entropy in reasoning has an ambiguous reliability meaning: it can reflect either non-viable uncertainty or benign solution diversity. To identify this phenomenon, we introduce a branch-viability diagnostic. Specifically, we record next-token alternatives from the privileged-answer teacher prompt, force each alternative after the student prompt plus its on-policy spine prefix, and test whether the resulting student-template continuation recovers the correct answer. On Qwen3-4B, we find that an oriented within-sequence position score is the strongest tested predictor of teacher-token reliability, reaching an area-under-ROC-curve (AUROC) of 0.83; local uncertainty scores are at most 0.57. Motivated by this trajectory-level structure, we propose Position-Weighted On-Policy Self-Distillation (PW-OPSD), which applies an increasing position weight while keeping the same student rollout, privileged teacher pass, and clipped forward-KL target as OPSD. In our comprehensive evaluations with different random seeds, the diagnostic-derived PW-OPSD improves AIME 2024 and AIME 2025 Avg@12 by +1.0 and +1.1 points, and a generalization evaluation on two larger-scale models from different families, DeepSeek-R1-Distill-Llama-8B and Olmo-3-7B-Think, also demonstrates consistent aggregate Avg@12 improvements. These results show that teacher-token reliability in reasoning distillation is trajectory-structured and can be utilized without additional teacher computation.

On-policy self-distillation, where a student is pulled toward a copy of itself conditioned on privileged context (e.g., a verified solution or feedback), offers a promising direction for advancing reasoning capability without a stronger external teacher. Yet in math reasoning the gains are inconsistent, even when the same approach succeeds elsewhere. A pointwise mutual information analysis traces the failure to the privileged context itself: it inflates the teacher's confidence on tokens already implied by the solution (structural connectives, verifiable claims) and deflates it on deliberation tokens ("Wait", "Let", "Maybe") that drive multi-step search. We propose Anti-Self-Distillation (AntiSD), which ascends a divergence between student and teacher rather than descending it: this reverses the per-token sign and yields a naturally bounded advantage in one step. An entropy-triggered gate disables the term once the teacher entropy collapses, completing a drop-in replacement for default self-distillation. Across five models from 4B to 30B parameters on math reasoning benchmarks, AntiSD reaches the GRPO baseline's accuracy in 2 to 10x fewer training steps and improves final accuracy by up to 11.5 points. AntiSD opens a path to scalable self-improvement, where a language model bootstraps its own reasoning through its training signal.

On-policy distillation (OPD) provides dense, per-token supervision for language model post-training, but its effectiveness is bottlenecked by teacher quality: external teachers suffer from distribution mismatch, while self-distillation with privileged conditioning is limited by in-context learning capacity. We propose RISE (Recursive Improvement via Self-Extrapolating Policy Distillation), which constructs a synthetic teacher directly from the model's own RLVR training trajectory. By extrapolating the displacement between the current checkpoint and a trailing anchor---in parameter space or output logit space---RISE converts a sparse outcome-induced parameter update into a dense token-level target, without any external model or privileged conditioning. RISE combines RLVR and OPD in a complementary loop: outcome rewards ground the extrapolation toward correct reasoning, while the extrapolated teacher refines token-level decisions. Moreover, since the teacher is refreshed every iteration as the student improves, distillation becomes a recursive improvement mechanism rather than a one-shot compression step. Experiments spanning mathematical reasoning, multi-domain STEM, code generation, and multi-turn agentic tasks show that RISE outperforms RLVR-only training and on-policy self-distillation across all settings.

On-policy distillation trains a language model on its own generations while a teacher scores them token by token. It combines the dense supervision of imitation learning with the on-policy sampling of reinforcement learning. But it requires a second, larger model to act as teacher. On-Policy Self-Distillation (OPSD) removes that cost. The teacher is the model itself, conditioned on privileged information the student will not have at test time, such as a reference solution, a plan, or environment feedback. The teacher is no stronger than the student, only better informed. Early results were promising, with accuracy comparable to reinforcement learning at a fraction of the generated tokens. But the same asymmetry that produces the signal also biases it. One failure mode now dominates the field: collapse, the progressive narrowing of the set of reasoning paths the model can produce. Collapse is not specific to OPSD, though privileged information aggravates it. This review treats collapse as a symptom governed by three levers: (i) where the signal is applied, that is, how tokens are weighted; (ii) what the teacher is shown, that is, the nature of the privileged information; and (iii) when the signal changes, that is, the teacher's dynamics and the decay of guidance. We restrict our scope to mathematical reasoning, where the method originated and where its failure modes are best documented. We report no new experiments. The contribution is structural: a shared vocabulary for phenomena named differently across papers, and a clear line between what is settled and what is still disputed.

Large reasoning models often solve problems through long chain-of-thought (CoT) traces, yet much of this computation is spent on redundant derivations, repeated self-verification, and detours that do not improve the final answer. Existing on-policy self-distillation methods reduce this cost by matching a student model to a concise copy of itself on prefixes sampled from the student's own rollouts. We show that this objective has an initialization bottleneck. Since supervision is applied only to visited prefixes, training from a verbose base model places the KL loss on contexts that are often noisy, redundant, or already off track. In such regions, a concise teacher can provide only local corrections, while the student continues to explore trajectories that an efficient reasoner should avoid. In this paper, we propose BIRD(Bootstrapped Iterative Self-Reasoning Distillation), a two-stage self-reasoning distillation method that improves the rollout distribution before on-policy training. BIRD first samples concise solutions from the base model under a brevity instruction, keeps only answer-correct traces, and performs a lightweight prompt-switch SFT step. The traces are generated with the brevity instruction but learned under the original task prompt, turning instruction-induced conciseness into a default reasoning behavior. Starting from this warm model, BIRD then applies on-policy reverse-KL distillation with a concise self-teacher, now on cleaner and more informative prefixes. Across Qwen3 series models, BIRD achieves a stronger accuracy-efficiency trade-off than prompting and cold-start on-policy distillation on MATH-500 and AIME benchmarks. On Qwen3-8B, it improves MATH-500 accuracy from 86.2% to 92.0% while reducing the average response length from 3,099 to 1,115 tokens. These results highlight prefix support as a central factor in efficient reasoning distillation.

On-policy distillation (OPD) supervises the student only in output space by matching next-token probabilities. This output-only paradigm has two limits: (1) sampling variance from Monte Carlo KL estimates over large vocabularies (e.g., Qwen's ~150k tokens) persists throughout training, and (2) it treats the teacher as a black-box, discarding all intermediate hidden states after the LM head. We propose On-Policy Representation Distillation (OPRD), which lifts distillation into hidden-state space by aligning student and teacher representations across selected layers on the same rollouts, bypassing the LM head entirely. Theoretically, OPRD eliminates sampling variance and provides richer per-layer structural information. Empirically, OPRD closes the student-teacher gap on AIME 2024/2025 and AIMO, while output-space OPD baselines plateau below the teacher. OPRD also trains 1.44x faster and uses 54% less memory than top-k OPD. Code: https://github.com/ShenzhiYang2000/OPRD.

On-policy self-distillation has become a strong recipe for LLM reasoning, where a privileged teacher supervises the student's own rollouts while conditioning on the reference solution. A design choice shared by nearly all such methods, however, has gone unquestioned: the teacher always sees the full reference reasoning. We argue that this default itself is part of the problem and identify a teacher-side exposure mismatch: when the teacher conditions on reasoning far beyond the student's current competence, the resulting token targets become too strong to absorb. A controlled fixed-exposure sweep makes this concrete on two fronts: 1) full exposure is not reliably the best choice, and 2) student-teacher mismatch grows monotonically as the teacher sees more privileged reasoning. This motivates treating teacher exposure not as a fixed hyperparameter but as a learnable training-time control variable. We therefore propose Adaptive Teacher Exposure for Self-Distillation (ATESD). ATESD models the reveal ratio with a lightweight Beta-policy controller conditioned on compact training-state statistics, and uses one sampled exposure for a short hold window of student updates. To make this exposure controller learnable, we optimize it with a discounted learning-progress reward that scores each held decision by its effect on the student's future improvement rather than its immediate loss change, addressing the delayed credit assignment induced by on-policy distillation. Experiments on AIME 24, AIME 25, and HMMT 25 across Qwen3-{1.7B, 4B, 8B} show that ATESD consistently outperforms competitive self-distillation and RL baselines, improving over OPSD by +0.95, +2.05, and +2.33 Average@12 points respectively, and establishing adaptive teacher exposure as an effective new axis for reasoning self-distillation.

We study multi-domain LLM training in which two models, each stronger in a different domain, co-evolve by tutoring each other through on-policy feedback. Unlike one-way distillation or single-model fine-tuning, our goal is mutual Pareto improvement: each model improves across domains without losing its original strength. To this end, we propose On-Policy Co-Distillation (OPCoD), where each student's self-distillation is conditioned on its own correct rollout and feedback from its peer. To make feedback exchange effective, OPCoD uses cognizance-based gating to decide when to give feedback and feedback anchoring to ground feedback in the problem. On Science Q\&A tasks, OPCoD consistently outperforms baselines and achieves Pareto improvement across all evaluated domain pairs and students.

We study on-policy distillation (OPD) for agentic tasks, where an LLM agent interacts with an environment over multiple turns and a student imitates a teacher over these multi-turn interaction histories. Fully online OPD is costly because each update requires fresh student rollouts through the environment and teacher queries at visited histories. We propose Replayed-Prefix On-Policy Distillation (ReOPD), an off-environment alternative that reuses pre-collected teacher trajectories as replayed prefixes: the student acts at selected steps, while the teacher provides dense per-step supervision without executing new environment interactions. We show that multi-turn OPD introduces a prefix trap: making histories more student-on-policy improves relevance to the student, but can query the teacher on histories where its target is unreliable. This creates a two-sided distribution shift between student occupancy and teacher reliability. ReOPD addresses this by treating multi-turn OPD as a reliability-aware prefix distribution design and implements it with a simple step-decaying sampling schedule that emphasizes early, lower-shift prefixes. Across mathematical reasoning with Python and search environments over multiple teacher and student model scales, ReOPD preserves or improves OPD-level accuracy, uses zero tool calls during student training, and is at least 4times faster per rollout than OPD. ReOPD therefore turns expensive agent-environment interaction into a reusable offline resource, enabling scalable distillation across tools, tasks, and environments.

Vision-Language-Action Models (VLAs) have demonstrated remarkable generalization capabilities in real-world experiments. However, their success rates are often not on par with expert policies, and they require fine-tuning when the setup changes. In this work, we introduce Refined Policy Distillation (RPD), a novel Reinforcement Learning (RL)-based policy refinement method that bridges this performance gap through a combination of on-policy RL with behavioral cloning. The core idea of RPD is to distill and refine VLAs into compact, high-performing expert policies by guiding the student policy during RL exploration using the actions of a teacher VLA, resulting in increased sample efficiency and faster convergence. We complement our method by fine-tuned versions of Octo and OpenVLA for ManiSkill3 to evaluate RPD in simulation. While this is a key requirement for applying RL, it also yields new insights beyond existing studies on VLA performance in real-world settings. Our experimental results across various manipulation tasks show that RPD enables the RL student to learn expert policies that outperform the VLA teacher in both dense and sparse reward settings, while also achieving faster convergence than the RL baseline. Our approach is even robust to changes in camera perspective and can generalize to task variations that the underlying VLA cannot solve. Our code, dataset, VLA checkpoints, and videos are available at https://refined-policy-distillation.github.io

On-policy distillation (OPD) trains a student on its own trajectories under token-level teacher supervision, but existing methods are capped by a single-teacher capability ceiling: when the teacher errs, the student inherits the error. OPD also remains largely unexplored in agentic tasks, where per-step errors compound across long trajectories and destabilize training. We propose MAD-OPD (Multi-Agent Debate-driven On-Policy Distillation), which breaks this ceiling by recasting the distillation teacher as a deliberative collective of teachers that debate over the student's on-policy state; the debate produces an emergent collective intelligence that supplies token-level supervision, with each teacher's contribution weighted by its post-debate confidence. To extend OPD to agentic tasks, we also introduce On-Policy Agentic Distillation (OPAD), which adds step-level sampling to stabilize training under multi-step error compounding. We additionally derive a task-adaptive divergence principle, selecting JSD (Jensen-Shannon divergence) for agentic stability and reverse KL (Kullback-Leibler) divergence for code generation, and verify it both theoretically and empirically. Across six teacher-student configurations (Qwen3 and Qwen3.5; 1.7B-14B students, 8B-32B teachers) and five agentic and code benchmarks, MAD-OPD ranks first across all six configurations; on the 14B+8Bto4B setting it lifts the agentic average by +2.4% and the code average by +3.7% over the stronger single-teacher OPD.

Reinforcement learning with verifiable rewards (RLVR) is central to improving long-CoT reasoning in large language models. Critic-free methods such as GRPO convert response-level rewards into advantages and uniformly broadcast them across tokens, overlooking their unequal contributions to the final outcome. On-policy self-distillation (OPSD) instead provides dense distributional supervision by minimizing the forward KL divergence between an unprivileged policy and a privileged self-teacher, implicitly assuming that the resulting likelihood shifts encode reliable answer-aligned information. We test this premise by fixing each sampled trajectory and re-scoring it under two opposing outcome conditions, one asserting correctness and the other incorrectness. Most affected tokens shift in the same direction under both conditions, with few sign reversals and substantial overlap in the induced optimization signals. Large shifts also concentrate on highly substitutable surface-form tokens, whereas tokens carrying problem-specific reasoning content are less sensitive. These findings show that privileged shifts fail to provide reliable answer-aligned directions, while their magnitudes primarily reflect counterfactual sensitivity rather than token-level learning value. Based on these observations, we propose Counterfactual Sensitivity Credit Reallocation (CSCR), a simple extension of GRPO that reduces credit for highly sensitive tokens and renormalizes token-level advantages to preserve both the original credit budget and verifier-determined direction. On long-CoT mathematical reasoning benchmarks, CSCR consistently outperforms GRPO baseline with the same number of policy updates. Targeted ablations further corroborate our diagnosis: privilege-induced directions are unreliable, moderate downweighting is most effective, and stronger modulation destabilizes optimization.

Medical Vision-Language Models (Med-VLMs) require reliable reasoning from fine-grained visual evidence, yet existing models can produce plausible clinical answers by relying on language priors or medical templates rather than truly attending to diagnosis-critical regions. On-Policy Distillation (OPD) offers dense token-level supervision on student-generated trajectories and provides a privacy-compatible means of capability transfer without requiring the redistribution of raw patient data. However, standard OPD uniformly distills all tokens, causing sparse evidence-dependent tokens to be diluted by abundant clinical narrative tokens. Inspired by the success of OPD in the large language model community, we propose Med-OPD, to our knowledge the first unified post-training framework that integrates on-policy distillation with medical evidence-aware supervision for Med-VLMs. We introduce Medical Evidence Advantage (MEA), a teacher-grounded counterfactual signal that uses an answer-aware hint to focus teacher scoring on evidence supporting the target diagnosis, and measures each token's dependence on medical visual evidence by comparing teacher likelihoods under the original and evidence-degraded imaging modalities. Based on MEA, Med-OPD redistributes the distillation signal at both the token and trajectory levels, emphasizing diagnosis-critical tokens and evidence-reliant rollouts. Experiments on OmniMedVQA subsets show that Med-OPD consistently outperforms SFT and standard OPD across CT, MRI, Disease Diagnosis, and Lesion Grading. These results demonstrate that evidence-aware distillation can better strengthen medical VLMs' reliance on key visual evidence and improve reliable multimodal medical reasoning. The source code and data is publicly available at: https://github.com/yunhang8658/MedOPD.git

On-policy distillation (OPD) offers superior capacity transfer by supervising student-sampled trajectories with dense token-level signals. To furnish high-quality supervision sources and thereby elevate the performance frontier of distillation, an intuitive direction is to infuse privileged information to either teacher or student itself. However, this additional input induces a potential failure mode we dub privilege illusion: a pattern that conflates the transferable capability gap that students are meant to close, and the information asymmetry gap that can only be mimicked but never replicated. This issue is further amplified by the inherent non-uniformity of token-level supervision, where only a small subset of tokens carries pivotal capability-bearing signals. To this end, we propose DOPD, an advantage-aware dual distillation paradigm that dynamically routes token-level supervision between privileged teacher and privileged student policies based on their advantage gap and relative probabilities. Each token receives supervision of different strength, objective, and strategy from either teacher or student itself, which transfers credible capability while simultaneously receiving auxiliary signals, to alleviate privilege illusion. Extensive experiments on both large language model (LLM) and vision-language model (VLM) settings demonstrate that DOPD consistently outperforms Vanilla OPD and other counterparts. Further results on stability, robustness, continual learning, and out-of-distribution tasks validate its superiority.

On-policy self-distillation has emerged as a promising paradigm for post-training language models, in which the model conditions on environment feedback to serve as its own teacher, providing dense token-level rewards without external teacher models or step-level annotations. Despite its empirical success, what this reward actually measures and what kind of credit it assigns remain unclear. Under a posterior-compatibility interpretation of feedback conditioning, standard in the implicit-reward literature, we show that the self-distillation token reward is a Bayesian filtering increment whose trajectory sum is exactly the pointwise mutual information between the response and the feedback given the input. This pMI can be raised by input-specific reasoning or by input-generic shortcuts, so we further decompose the teacher log-probability along the input axis. Based on this analysis, we propose CREDIT (Contrastive REward from DIsTillation), which isolates the input-specific component with a batch-contrastive baseline. At the sequence level, CREDIT is a teacher-side surrogate for a contrastive pMI objective that also penalizes responses remaining likely under unrelated inputs. Across coding, scientific reasoning, and tool-use benchmarks on two model families, CREDIT delivers the strongest aggregate performance at negligible additional compute.

On-Policy Self-Distillation (OPSD) is commonly interpreted as the transfer of privileged information: a teacher observes the verified solution to the target problem and supervises the student's trajectory. However, this interpretation conflates two effects. The reference solution not only reveals the answer to the current instance but also changes the context under which the teacher provides token-level supervision. We investigate the role of target-specific privilege with OP^{2}SD (On-Policy Self-Distillation from Other Problems), which replaces the paired reference with a problem and solution from a different example, while preserving the student rollout, teacher, and distillation objective. Across three models and three mathematics benchmarks, OP^{2}SD improves over the base model, remains competitive with OPSD. The success of OP^{2}SD implies that OPSD gains do not necessarily come from access to the reference solution, and that the teacher's context-induced behavior is an important factor.

Training small language-model agents for long-horizon interactive tasks requires both fast imitation and reward-driven improvement. On-policy distillation (OPD) provides dense teacher guidance and typically improves rapidly in the early stage, but its gains saturate once the student approaches the teacher, limiting the final performance ceiling. Reinforcement learning (RL) directly optimizes environment rewards and encourages exploratory improvement toward a higher reward-defined ceiling, but sparse and delayed feedback makes early-stage learning much less efficient than OPD. In this paper, we propose ATOD (Annealed Turn-aware On-policy Distillation), a hybrid online distillation algorithm that explicitly exploits this complementarity. (1) ATOD uses an annealed OPD-RL schedule: OPD dominates early training to approach teacher-level behavior, while RL is gradually strengthened to drive reward-based exploration. (2) ATOD introduces Turn-level Disagreement-Uncertainty Reweighting (T-DUR), which softly amplifies high-utility turns and improves dense supervision in long trajectories. Experiments on ALFWorld, WebShop, and Search-QA show that ATOD consistently outperforms competing post-training baselines: across the three student sizes, ATOD improves average success rate by 3.03 points over OPD and 23.62 points over GRPO, while surpassing the corresponding teacher models by 2.16 points.

Flow-matching models are now a mainstream method to image generation, but its adaptation to diverse downstream scenarios typically relies on post-training, which may cause conflicts among task-specific optimization objectives. Reinforcement learning enables direct optimization of task-specific rewards beyond the original models, yet trajectory-level optimization may incur high-variance gradients and cross-task interference. On-policy distillation (OPD) offers dense and stable supervision on student rollouts, but conventional teacher matching remains imitation-based. We propose DreOPD, a Degraded-reference extrapolative OPD method for flow-matching models that bridges these two paradigms. Our DreOPD converts implicit reward extrapolation into closed-form velocity regression, enabling extrapolative post-training with the stability of OPD. It further uses a mildly degraded reference to strengthen the teacher-reference contrast, yielding a clearer extrapolation direction. Experiments on single- and multi-teacher settings show that DreOPD outperforms OPD and multi-task RL baselines in average performance, while surpassing specialized teachers on most metrics.

Context distillation enables language models to internalize in-context knowledge into their parameters. In our work, we propose On-Policy Context Distillation (OPCD), a framework that bridges on-policy distillation with context distillation by training a student model on its own generated trajectories while minimizing reverse Kullback-Leibler divergence against a context-conditioned teacher. We demonstrate the effectiveness of OPCD on two important applications: experiential knowledge distillation, where models extract and consolidate transferable knowledge from their historical solution traces, and system prompt distillation, where models internalize beneficial behaviors encoded in optimized prompts. Across mathematical reasoning, text-based games, and domain-specific tasks, OPCD consistently outperforms baseline methods, achieving higher task accuracy while better preserving out-of-distribution capabilities. We further show that OPCD enables effective cross-size distillation, where smaller student models can internalize experiential knowledge from larger teachers.

On-Policy Distillation (OPD) has emerged as a dominant post-training paradigm for large language models, especially for reasoning domains. However, OPD remains unstable in practice due to the high gradient variance of its single-sample Monte Carlo estimator, and recipes for stable training are still immature. We propose vOPD (On-Policy Distillation with a control variate baseline), which casts OPD as policy-gradient RL and stabilizes it by introducing a control variate baseline-canonically a value function -- from the RL literature. We show that the OPD value function admits a closed form as the per-token negative reverse KL divergence between the student and the teacher, available directly from the already-computed forward pass with no additional critic or inference. Existing stabilization methods either compute the full token-level reverse KL over the entire vocabulary, adding significant overhead, or restrict it to a top-k support, biasing the objective. vOPD instead preserves the lightweight single-sample estimator, subtracting the value function as a detached baseline to keep the gradient unbiased while reducing variance. Furthermore, we show that a top-k approximation of the baseline further lowers cost without compromising performance. Across mathematical and scientific reasoning benchmarks, vOPD consistently outperforms vanilla OPD and matches the most expensive full-vocabulary baseline, offering an efficient stabilization of On-Policy Distillation through principled RL variance reduction.

Large language models are increasingly trained as interactive agents for long-horizon tasks involving multi-turn interaction, tool use, and environment feedback. Outcome-based reinforcement learning (RL) provides a practical optimization paradigm, but its sparse trajectory-level rewards offer limited guidance on intermediate decisions, leaving a supervision gap between episode-level outcomes and token-level policy learning. We propose SEED (SElf-Evolving On-Policy Distillation), a self-evolving framework that converts completed on-policy trajectories into training-time hindsight skills and distills their behavioral effect back into the policy model. SEED first fine-tunes the policy to analyze completed trajectories and generate natural-language skills that capture reusable workflows, decisive observations, or failure-avoidance rules. During RL, the current policy both collects trajectories and serves as the analyzer that extracts hindsight skills from them. Policy updates therefore improve subsequent decision making and skill analysis together, allowing hindsight supervision to evolve with the policy. SEED then re-scores the sampled actions under ordinary and skill-augmented contexts, converting the skill-induced probability shift into a dense token-level on-policy distillation signal. This signal is jointly optimized with outcome-based RL, keeping the auxiliary supervision aligned with the current trajectory distribution. Extensive experiments on text-based and vision-based agentic tasks show that SEED consistently improves performance and sample efficiency, exhibiting robust generalization to unseen scenarios. Our code is available at https://github.com/jinyangwu/SEED.

Autoregressive video generators are attractive for streaming, long-horizon, and interactive applications, but distilling strong black-box teachers into causal students remains difficult. The student must learn under its own rollout distribution, whereas practical teachers may expose only prompt-conditioned completed videos and may differ in architecture, capacity, temporal design, and sampling schedule. This interface makes supervised fine-tuning off-policy, score-based distillation inapplicable, and direct adversarial imitation too sparse for denoising-time credit assignment. We propose Adversarial Flow Distillation (AFD), an on-policy framework for heterogeneous black-box video distillation. AFD queries the teacher and rolls out the current student on the same prompts, trains a prompt-paired Bradley-Terry discriminator to estimate clean-sample teacher-student discrepancy, and converts the resulting on-policy advantage into forward-process flow-matching updates on the student's own noised states. Thus, AFD provides dense velocity-field supervision while requiring no teacher scores, latents, denoising trajectories, step alignment, or reverse-chain reinforcement learning. Experiments across two causal AR student families show that AFD consistently improves motion- and physics-sensitive generation while preserving general video quality, and ablations validate the importance of adaptive on-policy feedback and forward-process credit assignment. The method requires only clean teacher videos and student rollouts, providing a practical route for distilling proprietary or heterogeneous video generators into efficient autoregressive students.

Reinforcement learning with verifiable rewards (RLVR) has become a standard paradigm for post-training large language models (LLMs). While Group Relative Policy Optimization (GRPO) is widely adopted, it suffers from sparse reward signals and loses gradients entirely when all responses within a group receive identical rewards. On-policy distillation (OPD) offers a natural remedy by providing dense, token-level supervision from a teacher model. However, naively combining GRPO with OPD leads to degraded performance, due to three underlying causes: not all samples benefit from distillation; fitting too quickly to the teacher undermines the exploratory capacity of RL; and OPD's advantages are asymmetric, suppressing most tokens. To address these challenges, we propose RSTG (Recovering Learning Signals via Adaptive Teacher Guidance), which applies distillation selectively and precisely where it matters most. At the sample level, OPD is restricted to negative zero-variance prompts with each sample weighted by the teacher's confidence score. At the token level, distillation targets only tokens with high student entropy or large teacher-student divergence. We further augment training with SFT on correct trajectories generated by the teacher model, injecting positive gradient signals where RL yields none. Experiments demonstrate that RSTG substantially outperforms naive GRPO+OPD by +4.02% on math and +3.05% on code.

On-policy distillation (OPD) trains a student on prefixes sampled from its own policy while matching a stronger teacher. This addresses the prefix mismatch of offline distillation, but early student rollouts can still be poor, placing teacher supervision on weak or low-quality prefixes. We propose Trust-Region behavior Blending (TRB), a warmup method that replaces the early rollout policy with the closest-to-teacher behavior policy inside a student-centered KL trust region, while keeping the per-prefix reverse-KL OPD loss unchanged. The KL budget is annealed to zero, so training returns to pure student rollouts after warmup. Across two math-reasoning distillation settings, TRB attains the strongest average among the compared methods.

Knowledge distillation offers a promising path to transfer reasoning capabilities from large teacher models to efficient student models; however, existing token-level on-policy distillation methods require token-level alignment between the student and teacher models, which restricts the student model's exploration ability, prevent effective use of interactive environment feedback, and suffer from severe memory bottlenecks in reinforcement learning. We introduce On-policy Verbal Distillation (OVD), a memory-efficient framework that replaces token-level probability matching with trajectory matching using discrete verbal scores (0--9) from teacher models. OVD dramatically reduces memory consumption while enabling on-policy distillation from teacher models with verbal feedback, and avoids token-level alignment, allowing the student model to freely explore the output space. Extensive experiments on Web question answering and mathematical reasoning tasks show that OVD substantially outperforms existing methods, delivering up to +12.9% absolute improvement in average EM on Web Q&A tasks and a up to +25.7% gain on math benchmarks (when trained with only one random samples), while also exhibiting superior training efficiency. Our project page is available at https://OVD.github.io

Modern large language models (LLMs) can translate natural-language descriptions into operations research (OR) formulations. Post-training techniques including reinforcement learning and on-policy self-distillation have further improved this capability. However, three limitations remain in training LLMs for OR formulations. First, training commonly relies on synthetic formulations validated by human experts or stronger models, constraining scalable supervision. Second, credit assignment is either coarse or costly: outcome rewards score an entire trajectory without locating the responsible modeling decision, whereas process-level supervision requires an additional evaluator. Third, privileged self-distillation can induce style mismatch by using solver context unavailable at deployment. We find that a model can improve from solver-artifact feedback generated by its own rollouts, making self-distillation a practical, evaluator-free source of dense supervision. Therefore, we propose SOLID: Solver-Informed On-Policy LearnIng through Self-Distillation, a novel framework for self-improving OR language models without verified answers or external evaluators. SOLID executes candidate programs from multiple rollouts, clusters their objectives, and selects a majority-group artifact as a pseudo-reference. The model then performs updates using group-relative advantages and dense self-supervision signals. Across multiple OR benchmarks, SOLID improves solution accuracy for both general-purpose and OR-tuned models over outcome-only group-relative training. These results show that solver artifacts can support scalable self-improvement without trusted answers.

On-policy distillation (OPD), which supervises a student on its own sampled trajectories, has emerged as a data-efficient post-training method for improving reasoning while avoiding the reward dependence of reinforcement learning and the catastrophic forgetting often observed in standard supervised fine-tuning. However, standard OPD typically computes teacher supervision under noisy student-generated contexts and often relies on a single stochastic teacher rollout per prompt. As a result, the supervision signal can be high-variance: the sampled teacher trajectory can be incorrect, uninformative, or poorly matched to the student's current reasoning behavior. To address this limitation, we propose BRTS, a Best-of-N Rollout Teacher Selection framework for on-policy distillation. BRTS augments standard student-context OPD with a teacher-context supervision branch constructed from the curated teacher trajectory. Rather than distilling from the first sampled teacher rollout, BRTS samples a small pool of teacher trajectories and selects the auxiliary trajectory using a simple priority rule: correctness first, student alignment second. When multiple correct teacher trajectories are available, BRTS chooses the one most aligned with the student's current behavior; when unconditioned teacher samples fail on harder prompts, it invokes a ground-truth-conditioned recovery step to elicit a natural derivation. The selected trajectory is then used to provide reliable teacher-context supervision inside the OPD loop, augmented with an auxiliary loss on the teacher trajectory. Experiments on AIME 2024, AIME 2025, and AMC 2023 show that BRTS improves over standard OPD on challenging reasoning benchmarks, with the largest gains on harder datasets. Our code is available at https://github.com/BWGZK-keke/BRTS.

Consistency models have been proposed for fast generative modeling, achieving results competitive with diffusion and flow models. However, these methods exhibit inherent instability and limited reproducibility when training from scratch, motivating subsequent work to explain and stabilize these issues. While these efforts have provided valuable insights, the explanations remain fragmented, and the theoretical relationships remain unclear. In this work, we provide a theoretical examination of consistency models by analyzing them from a flow map-based perspective. This joint analysis clarifies how training stability and convergence behavior can give rise to degenerate solutions. Building on these insights, we revisit self-distillation as a practical remedy for certain forms of suboptimal convergence and reformulate it to avoid excessive gradient norms for stable optimization. We further demonstrate that our strategy extends beyond image generation to diffusion-based policy learning, without reliance on a pretrained diffusion model for initialization, thereby illustrating its broader applicability.

The ability to generate virtual environments is crucial for applications ranging from gaming to physical AI domains such as robotics, autonomous driving, and industrial AI. Current learning-based 3D reconstruction methods rely on the availability of captured real-world multi-view data, which is not always readily available. Recent advancements in video diffusion models have shown remarkable imagination capabilities, yet their 2D nature limits the applications to simulation where a robot needs to navigate and interact with the environment. In this paper, we propose a self-distillation framework that aims to distill the implicit 3D knowledge in the video diffusion models into an explicit 3D Gaussian Splatting (3DGS) representation, eliminating the need for multi-view training data. Specifically, we augment the typical RGB decoder with a 3DGS decoder, which is supervised by the output of the RGB decoder. In this approach, the 3DGS decoder can be purely trained with synthetic data generated by video diffusion models. At inference time, our model can synthesize 3D scenes from either a text prompt or a single image for real-time rendering. Our framework further extends to dynamic 3D scene generation from a monocular input video. Experimental results show that our framework achieves state-of-the-art performance in static and dynamic 3D scene generation.

On-Policy Distillation (OPD) improves the learning efficiency of standard reinforcement learning through dense, token-level supervision from teachers. In the standard KL objective of OPD, token-level losses are uniformly averaged, implying equal weights for all tokens. However, we discover that not all tokens are created equal: as student rollouts grow longer, they deviate further from the teacher's distribution, leading to degraded supervision quality at later positions. As a result, OPD using only the first 30% of tokens can perform comparably to using all tokens, whereas OPD using only the last 30% of tokens barely learns anything. In this work, we provide a principled understanding of this issue through the lens of constrained optimization. Based on these insights, we derive Importance-Weighted On-Policy Distillation (IW-OPD), in which the weight assigned to each token depends on the accumulated discrepancy between the student's and teacher's distributions, naturally upweighting earlier tokens and downweighting later ones with larger deviations. We show that IW-OPD converges significantly faster than OPD, with better learning efficiency, and achieves better final performance than standard OPD in both same-size and cross-scale settings, improving performance up to 6.9 points on AIME-2025.

On-policy distillation (OPD) trains student models under their own induced distribution while leveraging supervision from stronger teachers. We identify a failure mode of OPD: as training progresses, on-policy rollouts can undergo abrupt length inflation, causing truncated trajectories to dominate the training data. This truncation collapse coincides with abrupt repetition saturation and induces biased gradient signals, leading to severe training instability and sharp degradation in validation performance. We attribute this problem to the interaction between student-induced data collection and the distillation objective, which implicitly favors long and repetitive rollouts. To address this issue, we propose StableOPD, a stabilized OPD framework that combines a reference-based divergence constraint with rollout mixture distillation. These together mitigate repetition-induced length inflation and further stabilize OPD training. Across multiple math reasoning datasets, our approach prevents truncation collapse, stabilizes training dynamics, and improves performance by 7.2% on average.

On-policy distillation is an alternative post-training method in reinforcement learning that alleviates the constraints imposed by reward models by providing token-level supervision from a teacher model. Although on-policy distillation has been studied and applied across various settings, its fundamental design remains underexplored. In this paper, we introduce a new distillation reward, termed the delta signal, instead of directly imitating the teacher's output distribution. The delta signal is defined as the difference between the teacher model and its base model prior to instruction tuning for reasoning capability. It therefore captures the changes induced by reasoning tuning and provides a more direct signal for transferring reasoning capabilities. Using extensive empirical evidence, we show that the delta signal substantially improves on-policy distillation and refer to the new distillation method as On-Policy Delta Distillation (OPD^2). Experiments across mathematics, science, and code-reasoning benchmarks demonstrate that OPD^2 consistently outperforms conventional on-policy distillation, enabling reasoning LLMs to achieve strong performance with only a short post-training period. Code will be available at https://github.com/naver-ai/opd2

Pretrained video generators are promising visual world models that exhibit emergent task-solving abilities; however, their reliance on detailed textual descriptions limits their direct use for planning and decision-making. Existing approaches either outsource this reasoning to language or vision-language models, or rely on supervised fine-tuning with paired task-execution videos, which are costly to collect and difficult to scale. We propose a scalable framework that elicits task-solving ability in such models by combining self-distillation with reinforcement learning. Given an unlabeled scene image, a vision-language model generates a candidate task and a detailed step-by-step solution. The solution conditions a pretrained video diffusion model, the Demonstrator; we distill its behavior into an Executor conditioned only on the image and a short task prompt. This transfers execution knowledge from caption-guided generation to instruction-conditioned task solving without curated task-video supervision. We further improve the Executor with reinforcement learning from VLM feedback, exploiting the asymmetry between judging whether a sampled video satisfies a task and generating the solution. Experiments on our proposed WorldTasks-Benchmark and the DreamGen robotics benchmark show that the Executor surpasses the Demonstrator under our VLM-based evaluation protocol and transfers competitively to robotic tasks.

On-policy distillation (OPD) has become a core technique in the post-training of large language models, yet its training dynamics remain poorly understood. This paper provides a systematic investigation of OPD dynamics and mechanisms. We first identify that two conditions govern whether OPD succeeds or fails: (i) the student and teacher should share compatible thinking patterns; and (ii) even with consistent thinking patterns and higher scores, the teacher must offer genuinely new capabilities beyond what the student has seen during training. We validate these findings through weak-to-strong reverse distillation, showing that same-family 1.5B and 7B teachers are distributionally indistinguishable from the student's perspective. Probing into the token-level mechanism, we show that successful OPD is characterized by progressive alignment on high-probability tokens at student-visited states, a small shared token set that concentrates most of the probability mass (97%-99%). We further propose two practical strategies to recover failing OPD: off-policy cold start and teacher-aligned prompt selection. Finally, we show that OPD's apparent free lunch of dense token-level reward comes at a cost, raising the question of whether OPD can scale to long-horizon distillation.

On-policy distillation (OPD), which leverages a pre-trained, specialized teacher model to provide dense supervisory signals, has achieved significant success in Large Language Models (LLMs) and has recently been adapted to flow matching models. However, this paradigm suffers from two major issues: First, training a separate, task-specific teacher for every new objective incurs high computational costs. Second, the discrepancy between teacher and student distributions often leads to compounding errors along the generation trajectory. In this paper, we introduce Self-OPD, a teacher-free OPD framework for flow matching models that turns the student's own self-exploration into step-wise supervision. At each timestep, Self-OPD branches the deterministic next-state prediction into K stochastic SDE candidates, rolls them out with the ODE sampler, and compares their rewards against a deterministic self-reference baseline to obtain normalized advantages. The velocity field is optimized with an all-branch pull-push objective, where high-advantage branches attract the student and low-advantage branches repel it under direction-aware attenuation and SDE-variance normalization. For multi-objective alignment, Self-OPD fuses normalized scores at the reward level, avoiding direct gradient conflict. Experiments on single and mixed reward benchmarks show that Self-OPD outperforms prior RL and OPD methods without task-specific teachers.

Reinforcement learning with verifiable rewards (RLVR) has become a standard paradigm for post-training large language models. While Group Relative Policy Optimization (GRPO) is widely adopted, its coarse credit assignment uniformly penalizes failed rollouts, lacking the token-level focus needed to efficiently address specific deviations. Self-Distillation Policy Optimization (SDPO) addresses this by providing denser, more targeted logit-level supervision that facilitates rapid early improvement, yet it frequently collapses during prolonged training. We trace this late-stage instability to two intrinsic flaws: self-distillation on already-correct samples introduces optimization ambiguity, and the self-teacher's signal reliability progressively degrades. To resolve these issues, we propose Sample-Routed Policy Optimization (SRPO), a unified on-policy framework that routes correct samples to GRPO's reward-aligned reinforcement and failed samples to SDPO's targeted logit-level correction. SRPO further incorporates an entropy-aware dynamic weighting mechanism to suppress high-entropy, unreliable distillation targets while emphasizing confident ones. Evaluated across five benchmarks and two model scales, SRPO achieves both the rapid early improvement of SDPO and the long-horizon stability of GRPO. It consistently surpasses the peak performance of both baselines, raising the five-benchmark average on Qwen3-8B by 3.4% over GRPO and 6.3% over SDPO, while simultaneously yielding moderate response lengths and lowering per-step compute cost by up to 17.2%.

On-policy distillation (OPD), which aligns the student with the teacher's logit distribution on student-generated trajectories, has demonstrated strong empirical gains in improving student performance and often outperforms off-policy distillation and reinforcement learning (RL) paradigms. In this work, we first theoretically show that OPD is a special case of dense KL-constrained RL where the reward function and the KL regularization are always weighted equally and the reference model can by any model. Then, we propose the Generalized On-Policy Distillation (G-OPD) framework, which extends the standard OPD objective by introducing a flexible reference model and a reward scaling factor that controls the relative weight of the reward term against the KL regularization. Through comprehensive experiments on math reasoning and code generation tasks, we derive two novel insights: (1) Setting the reward scaling factor to be greater than 1 (i.e., reward extrapolation), which we term ExOPD, consistently improves over standard OPD across a range of teacher-student size pairings. In particular, in the setting where we merge the knowledge from different domain experts, obtained by applying domain-specific RL to the same student model, back into the original student, ExOPD enables the student to even surpass the teacher's performance boundary and outperform the domain teachers. (2) Building on ExOPD, we further find that in the strong-to-weak distillation setting (i.e., distilling a smaller student from a larger teacher), performing reward correction by choosing the reference model as the teacher's base model before RL yields a more accurate reward signal and further improves distillation performance. However, this choice assumes access to the teacher's pre-RL variant and incurs more computational overhead. We hope our work offers new insights for future research on OPD.

On-policy distillation (OPD), which aligns a student with the teacher's token-level distribution on the student's own rollouts, is an effective paradigm for transferring capabilities across LLMs. Prevailing approaches assume a teacher at least as capable as the student: they either distill a larger model into a smaller one, which fails at the frontier where no larger teacher exists, or consolidate multiple domain experts trained from a shared base, which requires costly training at the student's scale. We introduce Weak-to-Strong On-Policy Distillation (W2S-OPD), a simple yet effective OPD framework that improves the strong student by distilling from multiple weak models. W2S-OPD constructs a proxy teacher in logit space from a contrast pair of a positive and a negative model, both smaller than the student and cheap to obtain. Their logit difference isolates the capability direction, which is added to the student's own base model, yielding a proxy teacher that couples this direction while staying distributionally adjacent to the student. The student then distills it by minimizing the per-token reverse KL on its own rollouts. We instantiate the contrast pair as i) a post-RL expert against its pre-RL initialization, isolating the skill RL instills, ii) a larger against a smaller base model, isolating the capability from scale, and iii) a small base model with correct versus wrong hints, isolating the instance-level direction toward the solution. Across four math and three code benchmarks, W2S-OPD outperforms OPD, enables the student to surpass the domain teacher, and keeps improving the student even when every supervision source is weaker. Analysis shows different contrasts yield distinct signals: the post-RL and hint contrasts emphasize reasoning frameworks, while the scale contrast emphasizes the solving procedure. Our code will be available at https://github.com/Yu-Fangxu/W2S-OPD.

On-Policy distillation (OPD) transfers teacher capabilities by supervising student-sampled trajectories with dense token-level teacher signals. Recent selective OPD methods improve this process by prioritizing signals that are confident, informative, or learnable. However, the assumptions overlook a fundamental failure mode of language models: their token-level judgments can be driven by input-agnostic language priors, formatting conventions, or stereotyped reasoning templates rather than task-specific evidence. We refer to such optimization-relevant but weakly input-grounded supervision as spurious signals in OPD, which may produce large gradients while contributing little task-improving direction. To mitigate this issue, we propose SA-OPD, a Spurious-Signal-Aware On-Policy Distillation framework that identifies and filters misleading token-level supervision based on input-groundedness and optimization impact. SA-OPD introduces a lightweight input-groundedness proxy estimating whether a token-level distillation signal truly depends on the input. It then filters only tokens that simultaneously exhibit low input-groundedness and extreme distillation divergence, thereby removing high-impact spurious updates and achieving fine-grained OPD optimization. Extensive experiments on both large language model (LLM) and vision-language model (VLM) settings demonstrate that SA-OPD consistently outperforms Vanilla OPD and competitive selective methods. These results establish input-groundedness as a key dimension for OPD supervision selection and offer a simple, effective strategy for mitigating spurious updates.

On-policy distillation (OPD) has recently emerged as an important post-training paradigm. By using a stronger teacher model to provide dense, fine-grained supervision for sampled trajectories, OPD offers a clear advantage over reinforcement learning with verifiable rewards (RLVR), which typically depends on sparse binary or outcome-based environmental feedback. However, naive token-level distillation can suffer from gradient instability, due to magnitude misalignment in outlier states. To address this issue, we propose Globally Normalized Distillation Policy Optimization (GNDPO), a practical method that stabilizes optimization by transforming raw KL scores into batch-level relative advantages. This normalization effectively mitigates gradient explosions while retaining the benefits of token-level guidance. Experimental results show that GNDPO substantially improves training robustness and downstream performance across multimodal reasoning tasks. The code is released at https://github.com/OPPO-Mente-Lab/GNDPO.

Continual learning, enabling models to acquire new skills and knowledge without degrading existing capabilities, remains a fundamental challenge for foundation models. While on-policy reinforcement learning can reduce forgetting, it requires explicit reward functions that are often unavailable. Learning from expert demonstrations, the primary alternative, is dominated by supervised fine-tuning (SFT), which is inherently off-policy. We introduce Self-Distillation Fine-Tuning (SDFT), a simple method that enables on-policy learning directly from demonstrations. SDFT leverages in-context learning by using a demonstration-conditioned model as its own teacher, generating on-policy training signals that preserve prior capabilities while acquiring new skills. Across skill learning and knowledge acquisition tasks, SDFT consistently outperforms SFT, achieving higher new-task accuracy while substantially reducing catastrophic forgetting. In sequential learning experiments, SDFT enables a single model to accumulate multiple skills over time without performance regression, establishing on-policy distillation as a practical path to continual learning from demonstrations.

Text-to-image diffusion models produce impressive results but are frustrating tools for artists who desire fine-grained control. For example, a common use case is to create images of a specific instance in novel contexts, i.e., "identity-preserving generation". This setting, along with many other tasks (e.g., relighting), is a natural fit for image+text-conditional generative models. However, there is insufficient high-quality paired data to train such a model directly. We propose Diffusion Self-Distillation, a method for using a pre-trained text-to-image model to generate its own dataset for text-conditioned image-to-image tasks. We first leverage a text-to-image diffusion model's in-context generation ability to create grids of images and curate a large paired dataset with the help of a Visual-Language Model. We then fine-tune the text-to-image model into a text+image-to-image model using the curated paired dataset. We demonstrate that Diffusion Self-Distillation outperforms existing zero-shot methods and is competitive with per-instance tuning techniques on a wide range of identity-preservation generation tasks, without requiring test-time optimization.

State-of-the-art vision pretraining methods rely on image-level self-distillation from object-centric datasets such as ImageNet, implicitly assuming each image contains a single object. This assumption does not always hold: many ImageNet images already contain multiple objects. Further, it limits scalability to scene-centric datasets that better mirror real-world complexity. We address these challenges by introducing Object-level Self-DIStillation (ODIS), a pretraining approach that shifts the self-distillation granularity from whole images to individual objects. Using object-aware cropping and masked attention, ODIS isolates object-specific regions, guiding the transformer toward semantically meaningful content and transforming a noisy, scene-level task into simpler object-level sub-tasks. We show that this approach improves visual representations both at the image and patch levels. Using masks at inference time, our method achieves an impressive 82.6% k-NN accuracy on ImageNet1k with ViT-Large.

On-policy distillation (OPD) offers dense token-level supervision as an alternative to the sparse outcome-level advantages of reinforcement learning with verifiable rewards (RLVR). However, the teacher scores student-generated trajectories that are inherently off-policy for it, so the reliability of its supervision, and hence the source of the student's improvement, remains unclear. We quantitatively analyze teacher supervision during OPD training and find substantial noise whose prevalence increases with teacher scale. Surprisingly, the student policy is insensitive to such noise, converging to comparable performance regardless of whether noisy supervision is retained or removed. Does OPD distill at all? By analyzing what drives its gains, we find that learning concentrates on low log-probability tokens, and using a single fixed negative advantage matches the performance of teacher-provided ones. This suggests that OPD works largely by suppressing low log-probability tokens, which requires no teacher. These findings motivate On-Policy Self-Adaptation (OPSA), a supervision-free method using entropy-adaptive negative advantages. It assigns stronger learning signals to high-entropy positions, suppressing tail tokens, and evenly redistributing probability mass among head tokens. Compared with the base Qwen3-1.7B, OPSA improves Avg@32 by 35.41 points on AIME24, corresponding to a 263\% relative gain, and more than doubles Pass@32 across all three benchmarks. It also outperforms OPD by 16.77 points in Avg@32 on AIME24. Extensive experiments and analyses across model families and tasks further demonstrate its effectiveness and generalizability.

On-policy distillation (OPD) is increasingly used to improve large language model reasoning, but its training dynamics remain poorly understood. We characterize the trajectory of OPD updates in parameter space and compare it with supervised fine-tuning (SFT) and reinforcement learning with verifiable rewards (RLVR). A suite of parameter-space diagnostics consistently places OPD in a relaxed off-principal regime: compared with SFT, its updates affect fewer weights and avoid principal directions more strongly, while compared with RLVR, they remain less tightly constrained. Beyond this static localization, OPD exhibits subspace locking: its cumulative updates rapidly enter a narrow low-dimensional channel. Constraining training to the update subspace formed early in training preserves OPD performance but substantially degrades SFT, indicating that the locked subspace is functionally sufficient for OPD. Control experiments further show that sparsifying the update tokens and shifting rollout generation off-policy preserve the rank dynamics, whereas mixing the OPD objective with RLVR changes them. Overall, these results suggest that OPD is not merely an intermediate point between SFT and RLVR, but induces its own update geometry in parameter space.

On-Policy Distillation (OPD) is emerging as a promising alternative to reinforcement learning for LLM post-training, yet its effectiveness in multilingual settings remains underexplored. We study OPD and its advanced variant, On-Policy Delta Distillation (OPD^2), for mathematical reasoning in English, Korean, and Japanese. OPD^2 improves OPD by using the probability gap between a post-trained teacher and its base model as the learning signal. Experiments with Qwen3 show that OPD^2 consistently outperforms the original OPD, with particularly strong improvements in Korean and Japanese, and generally narrows the English-Korean performance gap. We further find that English-only OPD can also increase performance for Korean and Japanese, but often shifts the responses toward English, highlighting the importance of multilingual data to preserving target-language responses.

On-policy distillation (OPD) trains a student on its own rollouts with token-level supervision from teacher models, but its effectiveness can depend strongly on the warm-up stage before OPD. In this paper, we demystify warm-up for OPD from both data and training perspectives. For data, we find that effective warm-up relies on teacher-compatible chain-of-thought supervision, and that even incorrect teacher rollouts can provide comparable benefits to correct ones. This suggests that warm-up primarily transfers a teacher-compatible thinking pattern rather than merely correct answers. For training, we show that low-rank adaptation (LoRA) with a near-saturation training duration better balances in-domain adaptation and out-of-distribution generalization than full-parameter SFT. Based on these findings, we propose Simple-OPD, a plug-and-play initialization method that warms up the student on teacher-generated CoT with LoRA before OPD. Experiments across diverse settings demonstrate the effectiveness and robustness of Simple-OPD.

The growing capability of image generation models has made synthetic images a routine presence in open media, making robust and generalizable AI-Generated Image (AIGI) detection increasingly essential. While multi-modal large language models (MLLMs) offer a transparent alternative to black-box binary scoring, we observe that current MLLM-based detectors still exhibit notable perception bottlenecks in capturing fine-grained anomalies. They primarily focus on how visual evidence is organized and synthesized, leaving the intrinsic perception less optimized. To mitigate this gap, we present Veritas++, a perception-enhanced reasoning framework that establishes reliable perception as the foundation of authenticity reasoning. Rather than directly optimizing the model's explanatory ability, we ground AIGI detection on three basic perception abilities, i.e., capturing fine-grained visual details, semantic anomalies and pixel-level differences. Building on this insight, we introduce Perception-oriented Learning (PoRL), which replaces open-ended description supervision with verifiable rewards to explicitly strengthen these capacities. To further integrate enhanced perception with reasoning, we introduce Value-aware On-Policy Distillation (VaOPD), an adaptive distillation mechanism that prioritizes high-value distillation signals over uniform supervision, internalizing perception-aware reasoning through a privileged self-teacher. Extensive experiments across standard, in-the-wild and emerging benchmarks demonstrate that Veritas++ achieves promising generalization. The perception learning effectively bridges the perception gap and yields seamless gains on detection, while VaOPD further enables efficient capability evolvement without sacrificing existing performance. Code and checkpoints are available at https://github.com/EricTan7/VeritasPP.

On-policy distillation (OPD) combines student-generated rollouts with dense token-level supervision from a teacher. Existing work has mainly studied its algorithmic behavior, leaving the role of training data unclear. We examine this role at the data-minimal limit by training on a single query. One-shot OPD keeps improving for hundreds of steps and recovers most of full-data OPD's gain across task domains and model families. We explain this result through the states visited during training and the rate at which the student aligns with the teacher. We measure state coverage, the fraction of the states full-data OPD visits that a query set's rollouts reach. A single query already reaches \(71.5\%\), most of it within the first 100 steps. Adding semantically distinct queries raises coverage and validation accuracy together, until 16 queries reach \(98.9\%\) and match full-data training. Yet alignment slows at a similar pace whether OPD trains on one query or the whole dataset, and even a fixed set of states takes hundreds of steps to absorb. OPD is therefore data-overfed but algorithm-starved. Its rollouts quickly expose broad supervision, while the student absorbs that supervision increasingly slowly. The state-coverage result extends to multi-teacher OPD, where 16 semantically diverse queries per domain match full-data MOPD. As a further stress test, content-light templates and off-domain WildChat queries also approach the real-query baseline. Task content and induced state coverage can therefore come apart. We hope these findings direct future work toward the step efficiency of OPD, and prompt a re-examination of the data and the mechanisms behind its recent successes in frontier post-training.

Current post-training methods in verifiable settings fall into two categories. Reinforcement learning (RLVR) relies on binary rewards, which are broadly applicable and powerful, but provide only sparse supervision during training. Distillation provides dense token-level supervision, typically obtained from an external teacher or using high-quality demonstrations. Collecting such supervision can be costly or unavailable. We propose Self-Distillation Zero (SD-Zero), a method that is substantially more training sample-efficient than RL and does not require an external teacher or high-quality demonstrations. SD-Zero trains a single model to play two roles: a Generator, which produces an initial response, and a Reviser, which conditions on that response and its binary reward to produce an improved response. We then perform on-policy self-distillation to distill the reviser into the generator, using the reviser's token distributions conditioned on the generator's response and its reward as supervision. In effect, SD-Zero trains the model to transform binary rewards into dense token-level self-supervision. On math and code reasoning benchmarks with Qwen3-4B-Instruct and Olmo-3-7B-Instruct, SD-Zero improves performance by at least 10% over the base models and outperforms strong baselines, including Rejection Fine-Tuning (RFT), GRPO, and Self-Distillation Fine-Tuning (SDFT), under the same question set and training sample budget. Extensive ablation studies show two novel characteristics of our proposed algorithm: (a) token-level self-localization, where the reviser can identify the key tokens that need to be revised in the generator's response based on reward, and (b) iterative self-evolution, where the improving ability to revise answers can be distilled back into generation performance with regular teacher synchronization.

On-policy distillation (OPD) has shown strong potential for transferring reasoning ability from frontier or domain-specific models to smaller students. While effective on static single-turn tasks, its behavior in multi-turn agent settings remains underexplored. In this work, we identify a key limitation of vanilla OPD in such settings, which we term Trajectory-Level KL Instability. Specifically, we observe that KL divergence increases together with a drop in success rate, and even after convergence, the KL remains high, leading to unstable training. This instability arises from inter-turn error compounding: as errors accumulate, the student is driven beyond the teacher's effective support, rendering the supervision signal unreliable. To address this, we propose TCOD (Temporal Curriculum On-Policy Distillation), a simple yet effective framework that controls the trajectory depth exposed to the student and progressively expands it from short to long with a curriculum schedule.Experimental results across four student-teacher pairs on three multi-turn agent benchmarks (ALFWorld, WebShop, ScienceWorld) show that TCOD mitigates KL escalation and enhances KL stability throughout training, improving agent performance by up to 18 points over vanilla OPD. Further evaluations show that TCOD can even surpass the teacher's performance and generalize to tasks on which the teacher fails.

On-policy distillation (OPD) has become a key paradigm in LLM post-training, yet its training dynamics remain poorly understood. We present a systematic study examining the role, pathologies, and regulations of OPD. We first clarify the role of OPD as an exploration catalyst: it steers the student toward correct reasoning paths via dense token-level guidance, without expanding capability ceiling. We confirm this by showing that prompt diversity matters more than per-problem sampling numbers, and critically, that the effectiveness of OPD hinges entirely on the quality of its guiding signal. This dependency exposes two pathologies that derail exploration. The Student-Teacher Mismatch occurs when a large teacher-student distributional gap causes the guiding signal to misalign with task correctness, steering exploration in counterproductive directions. Length Exploitation arises when the aggregated token-level objective creates length-dependent shortcuts, allowing the student to game the reward landscape through response truncation or redundant padding, exploring degenerate length modes rather than reasoning strategies. To tame these pathologies, we investigate lightweight signal regulations: advantage clipping and log-scale compression, ensuring exploration is guided by faithful signals. Experiments across seven benchmarks demonstrate that these regulations alleviate length exploitation and enable effective distillation, stably surpassing OPD variants and RLVR baselines, thereby confirming that well-regulated signal quality, rather than mere teacher scale, governs successful exploration in OPD.

On-policy distillation (OPD) has become a central post-training tool for large language models (LLMs), providing dense per-token teacher supervision along the student's own rollouts. In this work, we identify a common structural cause underlying OPD, which we call prefix failure. Under prefix failure, dense per-token supervision induces a bimodal teacher mixture and fragmented gradients that token-level loss truncation or reweighting fail to address. This observation motivates us to move beyond token-level loss interventions toward trajectory-level output corrections. We thus propose Trajectory-Refined Distillation (TRD), a trajectory-level correction method that revises the student's rollout under the teacher guidance while within on-policy support. By correcting problematic prefixes before distillation, TRD mitigates prefix failure at its source. Moreover, TRD improves the exploration by exposing the student to alternative valid derivations under teacher guidance, even when the original rolls are already correct. TRD can also be applied to on-policy self-distillation (OPSD), a parameter-sharing variant that uses the student model conditioned on privileged informations as the teacher. Across a wide range of benchmarks and base models at multiple scales, TRD consistently outperforms prior baselines, improving single-attempt accuracy and broadening reasoning coverage. Code is available at https://github.com/louieworth/trd

On-policy distillation (OPD) is an increasingly important paradigm for post-training language models. However, we identify a pervasive Scaling Law of Miscalibration: while OPD effectively improves task accuracy, it systematically traps models in severe overconfidence. We trace this failure to an information mismatch: teacher supervision is formed under privileged context available during training, whereas the deployed model must report confidence using only deployment-time information. We formalize this perspective theoretically, showing that teacher-conditioned success is generally not a valid target for deployment-time confidence and that helpful privileged context induces entropy collapse and a systematic optimism bias. To address this, we propose a calibration-aware OPD framework, CaOPD, that estimates empirical confidence from model rollouts, replaces self-reported confidence with this student-grounded target, and distills the revised response through the same self-distillation pipeline. Experiments across various models and domains show that CaOPD achieves Pareto-optimal calibration while maintaining competitive capability, generalizing robustly under out-of-distribution and continual learning. Our findings highlight that capability distillation does not imply calibrated confidence, and that confidence should be treated as an essential objective in post-training. Code: https://github.com/SalesforceAIResearch/CaOPD

Reinforcement learning has emerged as a principled post-training paradigm for Temporal Video Grounding (TVG) due to its on-policy optimization, yet existing GRPO-based methods remain fundamentally constrained by sparse reward signals and substantial computational overhead. We propose Video-OPD, an efficient post-training framework for TVG inspired by recent advances in on-policy distillation. Video-OPD optimizes trajectories sampled directly from the current policy, thereby preserving alignment between training and inference distributions, while a frontier teacher supplies dense, token-level supervision via a reverse KL divergence objective. This formulation preserves the on-policy property critical for mitigating distributional shift, while converting sparse, episode-level feedback into fine-grained, step-wise learning signals. Building on Video-OPD, we introduce Teacher-Validated Disagreement Focusing (TVDF), a lightweight training curriculum that iteratively prioritizes trajectories that are both teacher-reliable and maximally informative for the student, thereby improving training efficiency. Empirical results demonstrate that Video-OPD consistently outperforms GRPO while achieving substantially faster convergence and lower computational cost, establishing on-policy distillation as an effective alternative to conventional reinforcement learning for TVG.

Enabling large language models to achieve stable self-improvement without external expert supervision remains a central challenge in complex reasoning tasks. Existing self-distillation and reinforcement learning methods lack explicit mechanisms for tracking problem-level learning progress and adapting optimization strategies accordingly. Consequently, training may over-optimize easy problems, receive weak supervision from hard problems, and fail to sufficiently explore borderline cases. To resolve these issues, we propose DRIFT, an online self-evolution policy optimization framework for large language models. DRIFT regulates the model's self-improvement process through the joint use of Difficulty Routing and Rhythm Gating. The former identifies the model's learning state at the problem level and dynamically allocates self-distillation and reinforcement learning signals, while the latter refines policy updates at the token level, concentrating exploration on critical reasoning positions. By further incorporating a success buffer and a two-stage curriculum learning strategy, DRIFT preserves high-quality historical experience while progressively guiding the model from reliable behavior acquisition toward stable policy evolution. Evaluated across five benchmarks and three model scales, DRIFT surpasses the peak performance of both GRPO and SDPO across all evaluated metrics. On the average score over the five benchmarks, DRIFT achieves 79.5%, outperforming GRPO by 9.5% and SDPO by 7.5%, establishing a new state-of-the-art result. Notably, on ToolUse, DRIFT reaches an accuracy of 79.2%, improving over GRPO by 13.5% and SDPO by 10.7%, setting a new state-of-the-art and substantially outperforming all concurrent methods.

On-Policy Distillation (OPD) is a fundamental technique for efficient post-training of large language models (LLMs), with broad applications in agent learning, multi-task enhancement, and model compression. However, OPD training becomes unstable when the teacher and student distributions differ substantially, as teacher supervision on student-generated tokens may yield unreliable policy gradients and even cause optimization failure. This work addresses reliable on-policy token-level supervision through credit assignment strategies, and proposes Trust Region On-Policy Distillation, TrOPD. It features the following characteristics: 1) Trust-Region On-Policy Learning: TrOPD performs OPD only in regions where the teacher provides reliable supervision, mitigating the optimization difficulty of the K1 reverse-KL estimator under distribution mismatch. 2) Outlier Estimation: For outlier regions, we explore gradient clipping, masking, and forward-KL estimation to reduce the adverse effects of unreliable supervision. 3) Off-Policy Guidance: The student continues generation from teacher prefixes and uses forward KL to imitate off-policy guidance, encouraging on-policy exploration toward reliable regions. Experiments show that TrOPD consistently outperforms SoTA OPD baselines, including OPD, EOPD, and REOPOLD, across mathematical reasoning, code generation, and general-domain benchmarks.

Privileged on-policy distillation improves multimodal reasoning by allowing a teacher to evaluate student trajectories using rich, training-only visual evidence. Both models score these trajectories while conditioning on the same student-generated prefix. When a student misinterprets an image early in a response, this accumulating erroneous rationale eventually pulls the teacher away from its visual evidence. The teacher and student converge on the same hallucination, causing standard cross-model supervision to collapse precisely where correction is most needed. We find that the teacher's visual corrective preference is not lost under this misleading agreement. Comparing the predictions of the identical teacher given the real image and a visual null reveals that the privileged evidence still pushes the model toward the correct interpretation. We introduce OPD-Aha, which reconstructs the distillation target directly from this isolated visual preference rather than relying on the fragile teacher-student discrepancy. This reconstructed target aggressively suppresses continuations that contradict the image. Trained with this objective, students learn to naturally interrupt their own flawed reasoning with reflection tokens such as wait and actually. After reflection, subsequent generation relies less on the accumulated erroneous text and more on the visual evidence. Correcting these trajectories mid-generation fundamentally alters the reasoning process, yielding broad and consistent improvements across diverse fine-grained perception and complex multimodal reasoning benchmarks. Our code and models are available at https://github.com/Echochef/OPD-Aha.

Reasoning models have advanced rapidly, but the dominant reinforcement learning from verifiable rewards (RLVR) recipe remains surprisingly narrow: sample many responses and reward each with a single bit indicating whether the final answer is correct. Yet many settings provide rich feedback, including execution traces, tool outputs, expert corrections, and model self-evaluations. We study how to use such feedback through a distributional variant of the classic imitation learning algorithm DAgger, where the learner has local access to an expert distribution on states visited by the current policy. This yields a simple forward cross-entropy objective that admits a blackbox expert and whose sequence-level gradient {conduct rich credit assignment by propagating} future expert-student disagreement back to earlier decisions. We show that prior RL with self-distillation objectives based on reverse KL or Jensen-Shannon fail to guarantee monotonic policy improvement: even when the expert has higher reward, their updates may increase probability on worse actions. In contrast, we show that forward cross-entropy admits monotonic policy improvement and enjoys guarantees on regret. We further show that our objective optimizes a lower bound on teacher-weighted likelihood of success, leading to improved Pass@N. Empirically, our approach, DistIL, improves over RLVR and RL with self-distillation baselines across a variety of domains: scientific reasoning, coding, and solving hard mathematical problems.

On-policy distillation has recently emerged as a promising alternative to standard sequence-level imitation, training a student by scoring its own rollouts with a teacher model. However, we observe ``Off-policy Teacher Decay'' problem in this paradigm: for the later tokens, with student's earlier trajectory as context that is off-policy to the teacher, the teacher's ability to produce a corrective score would decay, and may fall back to token-completion behavior learned in the pre-training stage. We empirically verify this problem, and we propose Early Stopping Rollout (ESR) to fix it: a simple yet effective distillation strategy that simply restricts the rollout generation to the first response tokens. We show that ESR both surpasses the full rollout OPD performance across model size, family, tasks and training regime, and exhibit much higher GPU efficiency and training stability, especially under cross model family scenarios. We further investigate the mechanism behind this surprising performance and discovered "Cascading Alignment" and "Sub-mode Commitment" effect of ESR that may explain why it works effectively and even sometimes exceeding the teacher model performance. Besides, we show that this position-based token selection strategy cannot be fully explainable by KL divergence and entropy signals.

Policies for complex visual tasks have been successfully learned with deep reinforcement learning, using an approach called deep Q-networks (DQN), but relatively large (task-specific) networks and extensive training are needed to achieve good performance. In this work, we present a novel method called policy distillation that can be used to extract the policy of a reinforcement learning agent and train a new network that performs at the expert level while being dramatically smaller and more efficient. Furthermore, the same method can be used to consolidate multiple task-specific policies into a single policy. We demonstrate these claims using the Atari domain and show that the multi-task distilled agent outperforms the single-task teachers as well as a jointly-trained DQN agent.

Black-box knowledge distillation for large language models presents a strict trade-off. Simple off-policy methods (e.g., sequence-level knowledge distillation) struggle to correct the student's inherent errors. Fully on-policy methods (e.g., Generative Adversarial Distillation) solve this via adversarial training but introduce well-known training instability and crippling computational overhead. To address this dilemma, we propose SODA (Semi On-policy Distillation with Alignment), a highly efficient alternative motivated by the inherent capability gap between frontier teachers and much smaller base models. Because a compact student model's natural, zero-shot responses are almost strictly inferior to the powerful teacher's targets, we can construct a highly effective contrastive signal simply by pairing the teacher's optimal response with a one-time static snapshot of the student's outputs. This demonstrates that exposing the small student to its own static inferior behaviors is sufficient for high-quality distribution alignment, eliminating the need for costly dynamic rollouts and fragile adversarial balancing. Extensive evaluations across four compact Qwen2.5 and Llama-3 models validate this semi on-policy paradigm. SODA matches or outperforms the state-of-the-art methods on 15 out of 16 benchmark results. More importantly, it achieves this superior distillation quality while training 10 times faster, consuming 27% less peak GPU memory, and completely eliminating adversarial instability.