On-Policy Distillation

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On-policy distillation studies how to transfer a teacher’s capabilities by training a student on trajectories the student generates, rather than only on fixed teacher-written examples. Common approaches match teacher and student token distributions with KL-style objectives, often combining this dense feedback with verifier rewards, reinforcement learning, or feedback from successful peer attempts. Work spans language-model reasoning and tool-using agents as well as multimodal, speech, diffusion, and embodied models; methods increasingly select useful tokens, turns, or rollout lengths to reduce compute. A central tension is that student-generated states can make supervision more relevant, but teacher signals may be unreliable or mismatched, and repeated rollouts can be costly or destabilize training. 4 sentences total.

Latest papers

507 papers177 papers in the last four weeks, up 139% on the four weeks before. 1.0% of all new papers.

Apr 29, 2026

Co-Evolving Policy Distillation

RLVR and OPD have become standard paradigms for post-training. We provide a unified analysis of these two paradigms in consolidating multiple expert capabilities into a single model, identifying capability loss in different ways: mixed RLVR suffers from inter-capability divergence cost, while the pipeline of first training experts and then performing OPD, though avoiding divergence, fails to fully absorb teacher capabilities due to large behavioral pattern gaps between teacher and student. We propose Co-Evolving Policy Distillation (CoPD), which encourages parallel training of experts and introduces OPD during each expert's ongoing RLVR training rather than after complete expert training, with experts serving as mutual teachers (making OPD bidirectional) to co-evolve. This enables more consistent behavioral patterns among experts while maintaining sufficient complementary knowledge throughout. Experiments validate that CoPD achieves all-in-one integration of text, image, and video reasoning capabilities, significantly outperforming strong baselines such as mixed RLVR and MOPD, and even surpassing domain-specific experts. The model parallel training pattern offered by CoPD may inspire a novel training scaling paradigm.

Naibin Gu, Chenxu Yang, Qingyi Si +7

Institute of Information Engineering, CAS, 2School of Cyber Security, UCAS, 3JD.COM

Reinforcement Learning with Verifiable Rewards Multi-Teacher Knowledge Distillation On-Policy Distillation RL Post-Training

Apr 27, 2026

TCOD: Exploring Temporal Curriculum in On-Policy Distillation for Multi-turn Autonomous Agents

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. Our code is available at https://github.com/kokolerk/TCOD.

Jiaqi Wang, Wenhao Zhang, Weijie Shi +2

Tongyi Lab , Alibaba Group · † The Chinese University of Hong Kong.

Language Model Distillation LLM Agents Curriculum Learning On-Policy Distillation Teacher-Student Learning

Apr 22, 2026

Learning from the Near Future: Temporal Self-Distillation for RLVR

Reinforcement learning with verifiable rewards (RLVR) is a core post-training recipe for reasoning models, yet pure on-policy learning can be inefficient when useful trajectories are difficult to discover or exploration narrows. Existing self-guided approaches largely reuse capability already available to the current or earlier learner. We instead ask whether learning can also make use of capabilities that emerge later in training: can a model learn from its own future self? We introduce temporal self-distillation, in which a policy receives guidance from a stronger later checkpoint of itself. We hypothesize that the most useful temporal teacher need not be the strongest one: a teacher must provide sufficiently new capability while remaining compatible enough for that capability to be readily transferred, motivating a near-future regime. We study this principle through two complementary mechanisms. Near-Future Policy Optimization (NPO) performs off-policy behavioral transfer using verified future-self trajectories, while Near-Future Policy Distillation (NPD) performs on-policy token-level transfer on learner-generated trajectories. We further introduce AutoNPO, which adaptively determines when temporal guidance is useful and how far to roll back, turning future-self guidance into a repeated self-bootstrap process. Across eight image-text benchmarks, NPO improves GRPO from 60.25 to 62.84 and AutoNPO reaches 63.15, with consistent gains on text-only and video reasoning. Under NPD, a near-future teacher reaches 63.23 after continued RL versus 61.92 with a far-future teacher, despite lower immediate post-distillation performance. Together, these results suggest that effective temporal self-distillation depends not simply on teacher strength, but on a balance between newly acquired capability and learner compatibility.

Chuanyu Qin, Chenxu Yang, Qingyi Si +6

Institute of Information Engineering, CAS · School of Cyber Security, UCAS

Reinforcement Learning with Verifiable Rewards Self-Distillation On-Policy Distillation Policy Learning Off-Policy RL

Apr 22, 2026

Hybrid Policy Distillation for LLMs

Knowledge distillation (KD) is a powerful paradigm for compressing large language models (LLMs), whose effectiveness depends on intertwined choices of divergence direction, optimization strategy, and data regime. We break down the design of existing KD methods and present a unified view that establishes connections between them, reformulating KD as a reweighted log-likelihood objective at the token level. We further propose Hybrid Policy Distillation (HPD), which integrates the complementary advantages of forward and reverse KL to balance mode coverage and mode-seeking, and combines off-policy data with lightweight, approximate on-policy sampling. We validate HPD on long-generation math reasoning as well as short-generation dialogue and code tasks, demonstrating improved optimization stability, computational efficiency, and final performance across diverse model families and scales. The code related to this work is available at https://github.com/zwhong714/Hybrid-Policy-Distillation.

Wenhong Zhu, Ruobing Xie, Rui Wang +1

Department of Computer Science and Engineering, Shanghai Jiao Tong University · Shanghai Innovation Institute · Large Language Department, Tencent

Language Model Distillation On-Policy Distillation Policy Distillation Knowledge Distillation

Apr 18, 2026

The Illusion of Certainty: Decoupling Capability and Calibration in On-Policy Distillation

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

Jiaxin Zhang, Xiangyu Peng, Qinglin Chen +3

Salesforce AI Research

On-Policy Self-Distillation Language Model Calibration On-Policy Distillation Language Model Post-Training

Apr 15, 2026

TIP: Token Importance in On-Policy Distillation

On-policy knowledge distillation (OPD) trains a student on its own rollouts under token-level supervision from a teacher. Not all token positions matter equally, but existing views of token importance are incomplete. We ask a direct question: which tokens carry the most useful learning signal in OPD? Our answer is that informative tokens come from two regions: positions with high student entropy, and positions with low student entropy plus high teacher--student divergence, where the student is overconfident and wrong. Empirically, student entropy is a strong first-order proxy: retaining

50\%

of tokens with entropy-based sampling matches or exceeds all-token training while reducing peak memory by up to

47\%

. But entropy alone misses a second important region. When we isolate low-entropy, high-divergence tokens, training on fewer than

10\%

of all tokens nearly matches full-token baselines, showing that overconfident tokens carry dense corrective signal despite being nearly invisible to entropy-only rules. We organize these findings with TIP (Token Importance in on-Policy distillation), a two-axis taxonomy over student entropy and teacher--student divergence, and give a theoretical explanation for why entropy is useful yet structurally incomplete. This view motivates type-aware token selection rules that combine uncertainty and disagreement. We validate this picture across three teacher--student pairs spanning Qwen3, Llama, and Qwen2.5 on MATH-500 and AIME 2024/2025, and on the DeepPlanning benchmark for long-horizon agentic planning, where Q3-only training on

<$$20\%

of tokens surpasses full-token OPD. Our experiments are implemented by extending the OPD repository https://github.com/HJSang/OPSD_OnPolicyDistillation, which supports memory-efficient distillation of larger models under limited GPU budgets.

Yuanda Xu, Hejian Sang, Zhengze Zhou +3

Knowledge Distillation On-Policy Distillation Selective Knowledge Distillation Uncertainty-Aware Knowledge Distillation

Apr 14, 2026

Rethinking On-Policy Distillation of Large Language Models: Phenomenology, Mechanism, and Recipe

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.

Yaxuan Li, Yuxin Zuo, Bingxiang He +8

Tsinghua University · ShanghaiTech University · University of Illinois Urbana-Champaign +1

Language Model Distillation On-Policy Distillation Knowledge Distillation Teacher-Student Learning

Apr 14, 2026

Lightning OPD: Efficient Post-Training for Large Reasoning Models with Offline On-Policy Distillation

On-policy distillation (OPD) is an effective post-training paradigm for large language models but requires a live teacher server throughout training, resulting in substantial infrastructure overhead. We investigate whether OPD can be performed offline by precomputing teacher log-probabilities once over SFT rollouts and reusing them during training. We find that naively doing so fails to reliably match standard OPD, and trace the root cause to a previously overlooked condition we term teacher consistency, requiring that the same teacher be used for both supervised fine-tuning and OPD. Violating this condition introduces a gradient bias that degrades performance for both offline and online OPD. Building on this insight, we propose Lightning OPD, an offline on-policy distillation framework that enforces teacher consistency and eliminates the need for a live teacher server entirely. We prove that, under teacher consistency, Lightning OPD shares the same optimum as standard OPD, with bounded gradient discrepancy and an implicit regularization effect that helps prevent policy drift. Experiments on math reasoning and code generation show that Lightning OPD achieves comparable performance to standard OPD while delivering 4.0x higher training efficiency. Starting from an SFT-initialized Qwen3-8B-Base model, Lightning OPD reaches 69.9% on AIME 2024 in just 30 GPU hours. Lightning OPD further scales to MoE architectures, training Qwen3-30B-A3B to 71.0% on AIME 2024 on a single 8xH100 node, substantially lowering the barrier for academic research on LLM post-training. Our code is released at https://github.com/jet-ai-projects/Lightning-OPD.

Yecheng Wu, Song Han, Han Cai

NVIDIA

On-Policy Distillation LLM Post-Training Teacher-Student Learning

Apr 12, 2026

SCOPE: Signal-Calibrated On-Policy Distillation Enhancement with Dual-Path Adaptive Weighting

On-policy reinforcement learning has become the dominant paradigm for reasoning alignment in large language models, yet its sparse, outcome-level rewards make token-level credit assignment notoriously difficult. On-Policy Distillation (OPD) alleviates this by introducing dense, token-level KL supervision from a teacher model, but typically applies this supervision uniformly across all rollouts, ignoring fundamental differences in signal quality. We propose Signal-Calibrated On-Policy Distillation Enhancement (SCOPE), a dual-path adaptive training framework that routes on-policy rollouts by correctness into two complementary supervision paths. For incorrect trajectories, SCOPE performs teacher-perplexity-weighted KL distillation to prioritize instances where the teacher demonstrates genuine corrective capability, while down-weighting unreliable guidance. For correct trajectories, it applies student-perplexity-weighted MLE to concentrate reinforcement on low-confidence samples at the capability boundary rather than over-reinforcing already mastered ones. Both paths employ a group-level normalization to adaptively calibrate weight distributions, accounting for the intrinsic difficulty variance across prompts. Extensive experiments on six reasoning benchmarks show that SCOPE achieves an average relative improvement of 11.42% in Avg@32 and 7.30% in Pass@32 over competitive baselines, demonstrating its consistent effectiveness.

Binbin Zheng, Xing Ma, Yiheng Liang +6

University of Science and Technology of China · Meituan LongCat Interaction Team · Nanjing University +2

On-Policy Distillation RL for Language Model Reasoning Step-Level Credit Assignment in RL Uncertainty-Aware Knowledge Distillation

Apr 9, 2026

Demystifying OPD: Length Inflation and Stabilization Strategies for Large Language Models

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.

Feng Luo, Yu-Neng Chuang, Guanchu Wang +4

Department of Computer Science, Rice University, Houston, USA · Department of Computer Science, University of North Carolina at Charlotte, Charlotte, USA · Department of Computer Science, Johns Hopkins University, Baltimore, USA +1

Repetition in Language Generation Language Model Distillation On-Policy Distillation Text Generation

Apr 9, 2026

On-Policy Distillation of Language Models for Autonomous Vehicle Motion Planning

Large language models (LLMs) have recently demonstrated strong potential for autonomous vehicle motion planning by reformulating trajectory prediction as a language generation problem. However, deploying capable LLMs in resource-constrained onboard systems remains a fundamental challenge. In this paper, we study how to effectively transfer motion planning knowledge from a large teacher LLM to a smaller, more deployable student model. We build on the GPT-Driver framework, which represents driving scenes as language prompts and generates waypoint trajectories with chain-of-thought reasoning, and investigate two student training paradigms: (i) on-policy generalized knowledge distillation (GKD), which trains the student on its own self-generated outputs using dense token-level feedback from the teacher, and (ii) a dense-feedback reinforcement learning (RL) baseline that uses the teacher's log-probabilities as per-token reward signals in a policy gradient framework. Experiments on the nuScenes benchmark show that GKD substantially outperforms the RL baseline and closely approaches teacher-level performance despite a 5

\times

reduction in model size. These results highlight the practical value of on-policy distillation as a principled and effective approach to deploying LLM-based planners in autonomous driving systems.

Amirhossein Afsharrad, Amirhesam Abedsoltan, Ahmadreza Moradipari +1

Stanford University · University of California, San Diego · University of California, Santa Barbara

Language Model Distillation Autonomous Driving Planning On-Policy Distillation

Apr 6, 2026

DP-OPD: Differentially Private On-Policy Distillation for Language Models

Large language models (LLMs) are increasingly adapted to proprietary and domain-specific corpora that contain sensitive information, creating a tension between formal privacy guarantees and efficient deployment through model compression. Differential privacy (DP), typically enforced via DP-SGD, provides record-level protection but often incurs substantial utility loss in autoregressive generation, where optimization noise can amplify exposure bias and compounding errors along long rollouts. Existing approaches to private distillation either apply DP-SGD to both teacher and student, worsening computation and the privacy--utility tradeoff, or rely on DP synthetic text generation from a DP-trained teacher, avoiding DP on the student at the cost of DP-optimizing a large teacher and introducing an offline generation pipeline. We propose Differentially Private On-Policy Distillation (DP-OPD), a synthesis-free framework that enforces privacy solely through DP-SGD on the student while leveraging a frozen teacher to provide dense token-level targets on student-generated trajectories. DP-OPD instantiates this idea via private generalized knowledge distillation on continuation tokens. Under a strict privacy budget (

\varepsilon=2.0

), DP-OPD improves perplexity over DP fine-tuning and off-policy DP distillation, and outperforms synthesis-based DP distillation (Yelp: 44.15

\rightarrow

41.68; BigPatent: 32.43

\rightarrow

30.63), while substantially simplifying the training pipeline. In particular, DP-OPD collapses private compression into a single DP student-training loop by eliminating DP teacher training and offline synthetic text generation. Code will be released upon publication at https://github.com/khademfatemeh/dp_opd.

Fatemeh Khadem, Sajad Mousavi, Yi Fang +1

Santa Clara University, Santa Clara, California, USA · Independent Researcher

Privacy-Preserving Language Models Privacy-Preserving ML On-Policy Distillation LLM Compression

Apr 4, 2026

SODA: Semi On-Policy Black-Box Distillation for Large Language Models

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.

Xiwen Chen, Jingjing Wang, Wenhui Zhu +7

Clemson University · LinkedIn · Washington University in St. Louis +2

Language Model Distillation Knowledge Distillation On-Policy Distillation

Apr 3, 2026

Self-Distilled RLVR

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.

Chenxu Yang, Chuanyu Qin, Qingyi Si +7

Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China · School of Cyber Security, University of Chinese Academy of Sciences, Beijing, China

On-Policy Self-Distillation Reinforcement Learning with Verifiable Rewards On-Policy Distillation

Apr 1, 2026

A Survey of On-Policy Distillation for Large Language Models

On-Policy Distillation (OPD) trains large language models with teacher guidance on student-generated trajectories, addressing the mismatch between fixed demonstrations and the histories encountered during deployment. As its use expands across language model training, different formulations of supervision and optimization make it difficult to compare methods and understand when they are effective. This survey develops a unified view of OPD through the interplay between student-generated states, teacher information, and policy updates. This framework connects the foundations of distillation with self-distillation, multi-teacher integration, reinforcement learning, and interactive agents. We examine how these settings change the supervision available to the student and relate the resulting design choices to capability transfer, training efficiency, and deployment. Our synthesis centers on the conditions under which guidance remains reliable and learnable as the student evolves, considering both immediate performance and the capacity for subsequent learning. We conclude by discussing open challenges in adapting supervision and allocating computation to support effective learning.

Mingyang Song, Mao Zheng

Large Language Model Department Tencent, China

Exposure Bias Language Model Distillation On-Policy Distillation Knowledge Distillation

Mar 27, 2026

VLA-OPD: Bridging Offline SFT and Online RL for Vision-Language-Action Models via On-Policy Distillation

Although pre-trained Vision-Language-Action (VLA) models exhibit impressive generalization in robotic manipulation, post-training remains crucial to ensure reliable performance during deployment. However, standard offline Supervised Fine-Tuning (SFT) suffers from distribution shifts and catastrophic forgetting of pre-trained capabilities, while online Reinforcement Learning (RL) struggles with sparse rewards and poor sample efficiency. In this paper, we propose On-Policy VLA Distillation (VLA-OPD), a framework bridging the efficiency of SFT with the robustness of RL. Instead of relying on sparse environmental rewards, VLA-OPD leverages an expert teacher to provide dense, token-level supervision on the student's self-generated trajectories. This enables active error correction on policy-induced states while preserving pre-trained general capabilities through gentle alignment. Crucially, we formulate VLA-OPD via a Reverse-KL objective. Unlike standard Forward-KL that induces mode-covering entropy explosion, or Hard-CE that causes premature entropy collapse, our bounded mode-seeking objective ensures stable policy learning by filtering out the teacher's epistemic uncertainty while maintaining action diversity. Experiments on LIBERO and RoboTwin2.0 benchmarks demonstrate that VLA-OPD significantly improves sample efficiency over RL and robustness over SFT, while effectively mitigating catastrophic forgetting during post-training.

Zhide Zhong, Haodong Yan, Junfeng Li +3

HKUST (GZ)

Vision-Language-Action Models On-Policy Distillation RL for VLMs

Mar 26, 2026

Revisiting On-Policy Distillation: Empirical Failure Modes and Simple Fixes

On-policy distillation (OPD) is increasingly used in LLM post-training because it can leverage a teacher model to provide dense supervision on student rollouts. The standard implementation, however, usually reduces distribution matching to a sampled-token log-ratio, which can make the learning signal fragile on long rollouts whose prefixes drift away from the teacher's typical support. We revisit this formulation from both theoretical and implementation perspectives. Theoretically, token-level OPD is biased relative to sequence-level reverse-KL minimization, but admits a substantially tighter worst-case variance bound; a controlled synthetic study further shows that stronger future-reward coupling increases gradient variance and destabilizes training. Empirically, we identify three failure modes of sampled-token OPD: imbalanced token-level supervision, unreliable teacher guidance on student-generated prefixes, and tokenizer or special-token mismatch. These findings motivate teacher top-K local support matching, a truncated reverse-KL objective that compares teacher and student distributions over a teacher-supported token set at each prefix, together with top-p rollout sampling and special-token masking. Across single-task reasoning and multi-task benchmarks spanning agentic and reasoning settings, this objective improves optimization stability and yields a +19.8% performance gain over standard sampled-token OPD baselines, providing a practical recipe for more stable on-policy distillation.

Yuqian Fu, Haohuan Huang, Kaiwen Jiang +4

State Key Laboratory of Multimodal Artificial Intelligence Systems, CASIA · School of Artificial Intelligence, UCAS · Fudan University +1

Language Model Distillation On-Policy Distillation

Mar 25, 2026

HDPO: Hybrid Distillation Policy Optimization via Privileged Self-Distillation

Large language models trained with reinforcement learning (RL) for mathematical reasoning face a fundamental challenge: on problems the model cannot solve at all - "cliff" prompts - the RL gradient vanishes entirely, preventing any learning signal from reaching these failure modes. We introduce Hybrid Distillation Policy Optimization (HDPO), which augments standard RL with privileged self-distillation targeting cliff prompts. On each training step, HDPO identifies prompts where all rollouts fail, generates privileged rollouts by providing the model with ground-truth information, filters for correct solutions, and distills the teacher's token-level distribution into the student. Because teacher and student share the same weights - differing only in their input - the realizability gap is provably bounded, unlike cross-model distillation. We prove that R=1 filtered privileged generation recovers the optimal KL-regularized RL policy in the hard-threshold limit. Experiments on OpenMathInstruct-2 with Qwen2.5-Math-1.5B-Instruct show that HDPO consistently improves coverage metrics (pass@4 by +0.8-1.1%, pass@8 by +0.4-1.7%) while maintaining greedy accuracy, with the distillation weight lambda providing direct control over the exploration-exploitation tradeoff.

Ken Ding

NVIDIA

RL for Language Model Reasoning LLM Reasoning On-Policy Distillation Self-Distillation

Mar 19, 2026

Nemotron-Cascade 2: Post-Training LLMs with Cascade RL and Multi-Domain On-Policy Distillation

We introduce Nemotron-Cascade 2, an open 30B MoE model with 3B activated parameters that delivers best-in-class reasoning and strong agentic capabilities. Despite its compact size, its mathematical and coding reasoning performance approaches that of frontier open models. It is the second open-weight LLM, after DeepSeekV3.2-Speciale-671B-A37B, to achieve Gold Medal-level performance in the 2025 International Mathematical Olympiad (IMO), the International Olympiad in Informatics (IOI), and the ICPC World Finals, demonstrating remarkably high intelligence density with 20x fewer parameters. In contrast to Nemotron-Cascade 1, the key technical advancements are as follows. After SFT on a meticulously curated dataset, we substantially expand Cascade RL to cover a much broader spectrum of reasoning and agentic domains. Furthermore, we introduce multi-domain on-policy distillation from the strongest intermediate teacher models for each domain throughout the Cascade RL process, allowing us to efficiently recover benchmark regressions and sustain strong performance gains along the way. We release the collection of model checkpoint and training data.

Zhuolin Yang, Zihan Liu, Yang Chen +14

RL for Language Model Reasoning RL for LLM Agents Reinforcement Learning Language Model Distillation On-Policy Distillation

Mar 11, 2026

Scaling Reasoning Efficiently via Relaxed On-Policy Distillation

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.

Jongwoo Ko, Sara Abdali, Young Jin Kim +2

On-Policy Distillation RL for Language Model Reasoning Sample-Efficient RL

Mar 7, 2026

Entropy-Aware On-Policy Distillation of Language Models

On-policy distillation is a promising approach for transferring knowledge between language models, where a student learns from dense token-level signals along its own trajectories. This framework typically uses reverse KL divergence, encouraging the student to match the teacher's high-confidence predictions. However, we show that the mode-seeking property of reverse KL reduces generation diversity and yields unstable learning signals when the teacher distribution has high entropy. To address this, we introduce Entropy-Aware On-Policy Distillation. Our key idea is augmenting the standard reverse KL objective with forward KL when teacher entropy is high, capturing the full range of plausible outputs while retaining precise imitation elsewhere. It balances mode-seeking precision with mode-covering robustness without sacrificing on-policy training efficiency. Experiments show that our method maintains generation diversity (sustained token-level entropy) and improves student-teacher alignment (lower forward KL on high-entropy tokens). Across six math reasoning benchmarks, this yields Pass@8 accuracy gains of +1.37 for Qwen3-0.6B-Base, +2.39 for Qwen3-1.7B-Base, and +5.05 for Qwen3-4B-Base compared to baseline on-policy distillation methods. These results demonstrate that accounting for teacher uncertainty is essential for maintaining diversity and achieving effective knowledge transfer.

Woogyeol Jin, Taywon Min, Yongjin Yang +5

KAIST AI, Seoul, South Korea · University of Toronto, Ontario, Canada · Vector Institute, Ontario, Canada +1

Language Model Distillation On-Policy Distillation Uncertainty-Aware Knowledge Distillation LLM Reasoning

Mar 6, 2026

X-OPD: Cross-Modal On-Policy Distillation for Capability Alignment in Speech LLMs

While the shift from cascaded dialogue systems to end-to-end (E2E) speech Large Language Models (LLMs) improves latency and paralinguistic modeling, E2E models often exhibit a significant performance degradation compared to their text-based counterparts. The standard Supervised Fine-Tuning (SFT) and Reinforcement Learning (RL) training methods fail to close this gap. To address this, we propose X-OPD, a novel Cross-Modal On-Policy Distillation framework designed to systematically align the capabilities of Speech LLMs to their text-based counterparts. X-OPD enables the Speech LLM to explore its own distribution via on-policy rollouts, where a text-based teacher model evaluates these trajectories and provides token-level feedback, effectively distilling teacher's capabilities into student's multi-modal representations. Extensive experiments across multiple benchmarks demonstrate that X-OPD significantly narrows the gap in complex tasks while preserving the model's inherent capabilities.

Di Cao, Dongjie Fu, Hai Yu +3

Tencent Hunyuan · Zhejiang University

Speech Language Models LLM Alignment Cross-Modal Knowledge Distillation On-Policy Distillation

Mar 5, 2026

CRISP: Compressed Reasoning via Iterative Self-Policy Distillation

Reasoning models often generate far more tokens than a task requires, which raises inference cost and can compound errors. We introduce CRISP (Compressed Reasoning via Iterative Self-Policy Distillation), an on-policy self-distillation method that teaches a model to reason more concisely by distilling its own concise behavior back into itself. The method uses a single idea: condition the same model on a "be concise" instruction to obtain teacher logits, then minimize the per-token reverse KL divergence between the student and this teacher on the student's own rollouts. It requires no ground-truth answers, no token budgets, and no difficulty estimators. The reverse-KL objective is naturally difficulty-adaptive: it compresses easy problems aggressively while preserving the reasoning steps that hard problems require. On Qwen3-14B, CRISP cuts reasoning length by up to 56% on MATH-500 and 38% on the harder AIME 2024, while improving MATH-500 accuracy by up to 3.3 points over the base model and holding AIME 2024 accuracy within about one point. This behavior generalizes across model sizes and families: Qwen3-8B shows the same compression with accuracy preserved, and DeepSeek-R1-Distill-Llama-8B improves accuracy on all five benchmarks while shortening its responses. General capabilities are preserved across all three models. Code is available at https://github.com/HJSang/OPSD_Reasoning_Compression.

Hejian Sang, Yuanda Xu, Zhengze Zhou +3

CoT Distillation Efficient Language Model Reasoning On-Policy Distillation CoT Compression LLM Reasoning

Mar 2, 2026

Surgical Post-Training: Proximal On-Policy Distillation for Reasoning with Knowledge Retention

Injecting new reasoning knowledge into Large Language Models (LLMs) via post-training often induces catastrophic forgetting. Recent studies emphasize the importance of on-policy data but suggest that KL-divergence fails to mitigate forgetting. In contrast, we show, both analytically and empirically, that the KL-constrained reward formulation actually plays a critical role in retaining knowledge during post-training. This motivates our Surgical Post-Training (SPOT), a proximal on-policy distillation framework designed to optimize reasoning efficiently while preserving prior knowledge. SPOT consists of (1) a data rectification pipeline employing an Oracle to surgically correct erroneous steps via minimal edits, generating proximal on-policy data; and (2) a reward-based binary cross-entropy objective essential for enhancing reasoning and mitigating forgetting. Empirically, with only 4k rectified math pairs, SPOT improves Qwen3-8B's accuracy by 6.2% on average across in-domain and out-of-domain tasks, requiring merely 16-minute model training on 8x H800 GPUs. Moreover, SPOT provides a superior initialization for subsequent reinforcement learning, significantly elevating the performance ceiling. Code: https://github.com/Visual-AI/SPoT

Wenye Lin, Kai Han

The University of Hong Kong

LLM Post-Training LLM Reasoning On-Policy Distillation Knowledge Distillation Continual Learning for LLMs

Feb 26, 2026

Reinforcement-aware Knowledge Distillation for LLM Reasoning

Reinforcement learning (RL) post-training has recently driven major gains in long chain-of-thought reasoning large language models (LLMs), but the high inference cost of such models motivates distillation into smaller students. Most existing knowledge distillation (KD) methods are designed for supervised fine-tuning (SFT), relying on fixed teacher traces or teacher-student Kullback-Leibler (KL) divergence-based regularization. When combined with RL, these approaches often suffer from distribution mismatch and objective interference: teacher supervision may not align with the student's evolving rollout distribution, and the KL regularizer can compete with reward maximization and require careful loss balancing. To address these issues, we propose RL-aware distillation (RLAD), which performs selective imitation during RL -- guiding the student toward the teacher only when it improves the current policy update. Our core component, Trust Region Ratio Distillation (TRRD), replaces the teacher-student KL regularizer with a PPO/GRPO-style likelihood-ratio objective anchored to a teacher--old-policy mixture, yielding advantage-aware, trust-region-bounded distillation on student rollouts and naturally balancing exploration, exploitation, and imitation. Across diverse logic reasoning and math benchmarks, RLAD consistently outperforms offline distillation, standard GRPO, and KL-based on-policy teacher-student knowledge distillation.

Zhaoyang Zhang, Shuli Jiang, Yantao Shen +6

AWS Agentic AI

Knowledge Distillation RL for Knowledge Distillation On-Policy Distillation Selective Knowledge Distillation RL for Language Model Reasoning

Feb 16, 2026

Fast and Effective On-policy Distillation from Reasoning Prefixes

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.

Dongxu Zhang, Zhichao Yang, Sepehr Janghorbani +6

Optum AI

Language Model Distillation On-Policy Distillation

Jan 29, 2026

OVD: On-policy Verbal Distillation

Knowledge distillation transfers reasoning capabilities from large teachers to efficient students. However, token-level on-policy distillation (OPD) constrains student exploration and requires teacher token probabilities, precluding distillation from black-box teachers that provide only text outputs. We introduce On-policy Verbal Distillation (OVD), a framework that uses verbal scores from black-box teachers to rank student-generated sub-trajectories, retaining high-scoring ones and replacing low-scoring ones with teacher-generated continuations. We analyze when ranking induced by verbal scores can guide distribution approximation: under a density-ratio calibration condition on acceptance probabilities and bounded teacher-replacement error, we bound the approximation error between the resulting mixed trajectory distribution and a teacher-preferred target. On Web Q&A, OVD achieves 41.09% average EM with teacher feedback at inference, exceeding the strongest evaluated baseline by 5.89 percentage points. On AMC23, OVD-FR improves accuracy over RLVR by 10.0 percentage points (52.5% to 62.5%) after 600 training steps on 128 problems. Further experiments suggest that retaining student-generated prefixes helps preserve exploration and mitigate trajectory-level entropy collapse. OVD also improves training efficiency: resampling selected suffixes rather than entire responses reduces mean per-step training time by 10.2% in the 128-problem setting. Project page: https://menik1126.github.io/ovd-project-page/.

Jing Xiong, Hui Shen, Shansan Gong +7

The University of Hong Kong, Hong Kong, China · Nanjing University, Nanjing, China · Huawei Technologies, China

Language Model Distillation On-Policy Distillation Teacher-Student Learning Knowledge Distillation