On-Policy Distillation

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Overview

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.

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511 papers178 papers in the last four weeks, up 141% on the four weeks before. 1.0% of all new papers.

Sep 23, 2026

When and Where to Trust the Teacher: Unifying On-Policy Distillation and GRPO through Entropy-Calibrated Credit Assignment

Reinforcement learning with verifiable rewards (RLVR) supervises mathematical reasoning through final-answer correctness, but provides little guidance on individual tokens. On-policy distillation (OPD) supplies dense feedback on student-generated responses, yet teacher preference need not reflect correctness. Recent hybrids combine OPD and verifier-derived advantages or reweight task credit using teacher ratios. However, teacher guidance enters after verifier-based group normalization, and token reweighting need not preserve the total task credit assigned to each response. We introduce Unified Entropy-Calibrated Credit Redistribution for GRPO (UECR-GRPO), which integrates verifier and teacher signals within a single GRPO-style update at both the response and token levels. Path-Utility Unification (PUU) combines verifier reward and a teacher-to-anchor path log-ratio in a single KL-regularized objective. Its on-policy implementation uses a length-normalized teacher score and combines both rewards before group normalization and PPO clipping, allowing teacher evidence to influence the response ranking. Entropy-Calibrated Redistribution (ECR) then uses the signed teacher--old-policy token gap to redistribute the verifier-derived component. Full-vocabulary teacher entropy attenuates uncertain guidance, while a response-wise zero-sum projection preserves the total task credit and its token-wise sign before clipping. Across five mathematical reasoning benchmarks, UECR-GRPO achieves average Avg@12\mathrm{Avg@12} accuracies of 17.21% and 65.09% with Qwen3-1.7B and Qwen3-4B students, respectively, exceeding the strongest baseline at each scale by 0.89 and 0.56 percentage points.

Jie Zhang, Jingxiao Yang, Zhehao Huang +2

Shanghai Jiao Tong University · Zhejiang University

RL for Language Model ReasoningGroup Relative Policy OptimizationCredit Assignment in RLReinforcement Learning with Verifiable RewardsOn-Policy Distillation
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Sep 23, 2026

RL Starts before RL: On Policy Distillation for Better Reinforcement Learning

Reinforcement learning (RL) improves reasoning, but its performance depends on the policy from which training begins. We study on-policy distillation (OPD) as a preparation stage for RL and ask whether its benefits extend beyond improvements in the distilled model's initial accuracy. Under shared RL settings, students initialized with OPD reach higher final performance than those trained with direct RL or supervised fine-tuning followed by RL. This advantage can emerge even when OPD produces little immediate improvement in accuracy. Pre-RL Pass@k does not fully explain the benefit: similar or even higher values do not necessarily lead to better performance after RL. Behavioral analyses point to alignment with the teacher's distribution beyond top-1 agreement as a possible explanation. Such alignment may favor higher-quality reasoning paths while retaining alternatives that RL can further refine using outcome feedback. We further examine how trajectory sources and divergence objectives affect the value of distillation for subsequent RL. Standard reverse-KL OPD performs better before RL, but forward-KL OPD overtakes it afterward. Student rollouts outperform teacher rollouts under both objectives before and after RL. These findings highlight the importance of both objective choice and the states receiving supervision for subsequent RL. Our results support OPD as preparation for RL and favor forward KL when OPD is followed by RL in our comparison.

Shuai Dong, Yongfu Zhu, Yuqi Xu +26

Fudan University · SII · Peking University +2

Reinforcement LearningRL for Language Model ReasoningOn-Policy DistillationRL Post-Training
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Sep 23, 2026

Counterfactual Constraint-Conditioned On-Policy Distillation for Multi-Constraint Instruction Following

Multi-constraint instruction following requires a model to respond to a query under many simultaneously active constraints. Even strong instruction-tuned models still routinely violate some of them. Existing approaches either augment supervision with sequence- or token-level RL rewards from external verifiers or learned graders, or use on-policy distillation (OPD) against a single full-context teacher whose probability mass becomes diluted as more constraints become simultaneously active. We propose CC-OPD (Counterfactual Constraint-Conditioned On-Policy Distillation), which inverts the standard supervision-generation direction in distillation. Rather than enriching the teacher with information beyond what the student sees, CC-OPD ablates each constraint from the teacher's conditioning in turn, and constructs the per-constraint signal from the resulting per-token probability differentials. The resulting per-token leave-one-out log-likelihood shifts are summed, clipped, and added to the vanilla OPD reward as a token-level shaping term. All shaping terms are obtained from the frozen teacher, without an external verifier during distillation, and the reward equals vanilla OPD wherever the aggregate shift is zero. Across two Qwen model pairs and seven benchmarks, CC-OPD achieves the highest average among all evaluated student-training methods. A 1.5B student trained with CC-OPD surpasses its own 7B RL-trained teacher on the MulDimIF benchmark.

Yanzhao Zheng, Yuanqiang Yu, Tianze Xu +6

Alibaba Group, Hangzhou, China

Reward ShapingInstruction FollowingLanguage Model DistillationOn-Policy Distillation
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Sep 22, 2026

Train Where the Quantized Model Goes: On-Policy Distillation for Low-Bit Reasoning

Quantization-aware distillation (QAD) restores much of the short-form question-answering performance lost to sub-3-bit quantization, yet leaves mathematical and code reasoning substantially impaired. Long generations often degenerate into repetitive loops, exhausting the decoding budget without completing a solution. We trace this gap to quantization-amplified exposure bias: QAD trains on fixed corpus prefixes, while quantization-induced deviations compound along the model's own autoregressive trajectories. To address this mismatch, we introduce an on-policy distillation (OPD) stage that places teacher supervision where the quantized model actually goes. Starting from a QAD checkpoint, the student generates through the quantized forward path used at deployment and receives feedback from a frozen full-precision teacher on its own prefixes, combining dense token-level guidance with task-verifier rewards. Across four models at 2.79 and 1.88 effective bits, OPD raises average BF16 performance retention from 35% to 70% on MATH-500 and from 66% to 91% on HumanEval while preserving short-form performance, with reasoning gains substantially exceeding those of continued teacher-forced QAD in matched-budget comparisons. By coupling QAD's stable low-bit initialization with OPD's on-policy reasoning recovery, our framework provides a comprehensive sub-3-bit solution that preserves broad capabilities while restoring long-form reasoning.

Yuanteng Chen, Zhilei Liu, Peisong Wang +7

Institute of Automation, Chinese Academy of Sciences · School of Artificial Intelligence, University of Chinese Academy of Sciences · Zhongguancun Academy +2

Low-Bit QuantizationLLM QuantizationQuantization-Aware TrainingCode GenerationMathematical ReasoningOn-Policy Distillation+2
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Sep 22, 2026

BAS-OPD: Budget-Aware Selective On-Policy Self-Distillation for Fine-Grained Multimodal Perception

Multimodal large language models (MLLMs) often struggle with fine-grained visual perception when processing complete images, as critical evidence may only appear in local regions. On-policy self-distillation (OPD) enables transferring privileged visual knowledge from informative views to full-image policies, but querying the teacher for every rollout introduces substantial supervision costs. In this work, we propose BAS-OPD, a budget-aware selective OPD framework that allocates teacher supervision under limited query budgets. Instead of querying all rollouts, BAS-OPD selects informative samples while maintaining full-batch student generation. We explore random, uncertainty-based, and learned utility-based selection strategies, where the learned selector estimates query value from detached rollout statistics and online utility signals derived from student--teacher agreement and teacher confidence without additional student forward passes. BAS-OPD only changes training-time supervision allocation and preserves single-pass full-image inference. Experiments on fine-grained multimodal perception benchmarks demonstrate that BAS-OPD achieves strong performance while substantially reducing teacher supervision costs, highlighting the effectiveness of selective OPD under constrained budgets.

Zihan Chen, Hengguang Zhou, Yuan Kang +5

HFIPS, Chinese Academy of Sciences · University of Science and Technology of China · University of California, Los Angeles

VLM DistillationMultimodal Large Language ModelsOn-Policy DistillationKnowledge DistillationFine-Grained Visual Perception
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Sep 21, 2026

iSDFT: Information-Proximal Self-Distillation for Continual Learning in LLMs

On-policy self-distillation fine-tuning (SDFT) learns new skills from demonstrations while reducing forgetting, but it always distils toward the full demonstration-conditioned teacher. This fixes teacher influence at the full-teacher endpoint, providing no control over how much demonstration information should be transferred at each prediction state. We introduce Information-Proximal SDFT (iSDFT), which instead treats the teacher as a budgeted source of information. At each token, iSDFT selects the distribution closest to the current student that satisfies a prescribed teacher-information constraint, yielding a closed-form exponential target with a locally determined tilt. To control cumulative drift, we further anchor the student to its frozen base policy. Across four heterogeneous LLM backbones and two specialisation tasks, iSDFT improves vanilla SDFT in 7 of 8 model-task settings and matches it in the remaining one. It also provides tighter retention on the original SDFT benchmark suite, with 73% of evaluations remaining within 0.5 points of the base model versus 52% for the strongest baseline, while achieving the largest mean improvement on all ten additional mathematics, coding, and competition-mathematics benchmarks. These results show that controlling how much and when teacher information is introduced improves specialisation while preserving broader capability.

Ahmed Khaled Khamis, Xiaotong Ji, Hassan Jaber +4

Imperial College London · Politecnico di Torino · UCL Centre for AI

Continual Learning for LLMsLanguage Model DistillationOn-Policy DistillationKnowledge Distillation
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Sep 21, 2026

1% of Tokens Can Be Enough: On Gradient Estimation in On-Policy Distillation

Sparse on-policy distillation (OPD) allocates teacher supervision to a small subset of tokens in student-generated trajectories. However, useful teacher guidance can yield a noisy update when its gradient is estimated from a sampled next token. We study this estimation problem at a fixed prefix in information geometry and propose an information-efficiency ratio (IER) based on a signal-to-noise decomposition. IER characterizes relative gradient estimation error under an optimal scalar baseline. A candidate-set approximation enables token selection based on IER and its combination with existing usefulness scores, while retaining the sampled reverse-KL training objective. On mathematical and medical reasoning tasks, adding IER improves existing selectors in multiple settings, with sparse configurations matching or exceeding full OPD without token selection at small token budgets of 0.1%--1%. These results support accounting for both usefulness and gradient-estimation reliability when allocating sparse supervision. Our code is available at https://github.com/BruceSheng1202/IER-OPD.

Huanxin Sheng, Zhiling Ye, Haonan Wang +3

MBZUAI · Ant Group

On-Policy Distillation
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Sep 21, 2026

CLOOPD: Closing the Learner Loop in On-Policy Distillation

On-policy distillation (OPD) pays twice for each fresh batch: the student generates trajectories and a stronger teacher scores them. Existing methods improve which trajectories are scored and how the teacher signal is constructed, but usually consume it with one actor update. We introduce CLOOPD, a closed-loop framework separating teacher-signal acquisition from student-side realization. CLOOPD selects an adaptive αα waypoint inside a KL envelope, freezes the scored batch and its advantages, re-forwards the student after each actor pass, measures realization, and allocates actor work under a separate token budget. The framework includes deterministic two- and three-pass policies, token-priced CLOOPD-TPMR, and a budget-matched control. Across six 300-step runs on an 8-H20 node, every CLOOPD policy improves the one-pass TOP-D anchor at comparable teacher-token scale: macro accuracy rises from 15.41 to 17.78 with CLOOPD-Fixed2 and 19.36 with CLOOPD-Fixed3. At step 100, CLOOPD-Fixed3 reaches 15.35, nearly matching TOP-D at step 300 while using 67.2% fewer teacher-scored tokens and 28.0% fewer GPU-hours. Earlier 8-A100 ablations show adaptive αα eliminates observed trust-envelope violations; a third pass adds headroom. These results position CLOOPD as a framework for budgeting how fully students learn from teacher-scored tokens.

Keye Zheng, Hanyu Li, Zhan Cheng +1

Alibaba Group

Language Model DistillationOn-Policy DistillationKnowledge Distillation
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Sep 20, 2026

Distill What You Trust: Reliability-Aware Multi-Teacher On-Policy Distillation

Multi-teacher on-policy distillation allows a student to learn from complementary specialists on its own trajectories. Domain-routed approaches, however, select one teacher per example and keep it fixed throughout the response. This design both depends on domain labels that mixed training corpora often lack and cannot adapt teacher selection when the expertise required changes within a trajectory. We observe that each specialist deviates more from a shared reference on in-domain prompts than on out-of-domain prompts, on average. Based on this observation, we propose TrustMOPD, which replaces example-level teacher selection with label-free, token-level supervision allocation. At each student-generated prefix, TrustMOPD measures this displacement in next-token preferences, calibrates its magnitude across teachers, and uses the resulting scores as proxies for local reliability to weight teacher-specific distillation losses. Evaluated across mathematics, code, and instruction following, TrustMOPD closes 91.5% and 98.0% of the overall-score gap between the initial student and oracle-routed teachers when trained on SingleCap and MultiCap, respectively, compared with 54.4% and 54.5% for the strongest label-free baseline in each setting. On SingleCap, it approaches label-based MOPD without using domain labels. Our code is available at https://github.com/sunjie279/TrustMOPD-.

Jie Sun, Mao Zheng, Mingyang Song +8

University of Science and Technology of China · Foundation Model Department, Tencent · Tsinghua University +4

Language Model DistillationMulti-Teacher Knowledge DistillationOn-Policy DistillationKnowledge Distillation
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Sep 20, 2026

Tool-Augmented On-Policy Distillation for LLM Domain Adaptation in Sequence-Based Omics Tasks

Multi-omics sequences contain complex biological patterns, yet deciphering their mechanisms for automated scientific discovery remains challenging. As large language models (LLMs) interpret these sequences, evaluating both predictions and scientific reasoning is critical. However, existing benchmarks for multi-omics sequence tasks rely on classification and regression metrics, neglecting whether models grasp the underlying biological evidence. We introduce OmicsBench, the first reasoning benchmark for multi-omics sequences, comprising 1,160 expert-validated questions across six tasks spanning DNA regulation, RNA processing, and protein function. OmicsBench requires traceable evidence chains, evaluated using instance-specific rubrics developed with domain experts. Evaluating 17 LLMs reveals an inverse relationship: while scientific LLMs outperform general-purpose LLMs in sequence classification accuracy, they fail to provide valid evidence to support their predictions. One plausible interpretation is shortcut learning: specialized models may rely on statistical patterns rather than the biological mechanisms needed for scientific discovery. Motivated by this finding, we introduce tool-augmented on-policy distillation (TA-OPD), a post-training method to align sequence prediction with evidence-grounded biological reasoning. Across five Qwen3.5 models spanning 0.8B to 27B parameters, TA-OPD consistently strengthens biological evidence grounding while improving predictive performance on most tasks. These gains persist across model scales, indicating that stronger sequence reasoning does not arise solely from increased model capacity, but can be improved through evidence-aware training. Together, OmicsBench and TA-OPD provide a framework for diagnosing reasoning failures in multi-omics LLMs and a path toward models whose predictions are better grounded in biologically meaningful evidence.

Jie Ying, Zhefan Wang, Zihong Chen +11

Shanghai Artificial Intelligence Laboratory · Yazhouwan National Laboratory · Shanghai Innovation Institute +2

LLM EvaluationOn-Policy DistillationGenomicsScientific Reasoning in Language Models
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Sep 20, 2026

One to More, More to One: Category-Aware Iterative Expert Training for Software Engineering Agents

Repository-level software engineering (SWE) comprises heterogeneous task categories, whose progress under pooled agentic reinforcement learning can be uneven: gains in some categories coincide with regressions in others, while aggregate resolution obscures these changes. Motivated by this category see-saw, we develop a category-aware expert-training and policy-integration framework. Executable task construction and SWE Labeler, an evidence-grounded multi-axis labeling system, organize the training pools. Initial category-specific RL improves average training success while leaving uneven instance-level progress, motivating explicit consolidation of successful behavior and policy-adaptive task selection. Same-origin category experts alternate long-horizon Agentic-miniRL with Refresh-Repair-Expand (RRE): the updated policy refreshes instance mastery, reuses its own verified successful trajectories for Repair SFT, and reselects tasks for further RL. Label-routed multi-teacher on-policy distillation (MOPD) consolidates the experts into one deployable student, with ReLU-gated reward extrapolation keeping only each teacher's improving direction over the reference. Expert training and policy integration require no external model to provide solution trajectories or action targets. We evaluate Pooled RL and Balanced RL, expert development, and single-model integration through aggregate and per-category resolution, the minimum category lift over each joint-RL baseline, and expert-gain recovery. The final MOPD policy achieves mean resolution of 58.04% on Pro-618 and 59.00% on SWE-bench Multilingual, improving over the base model by 5.39 and 2.78 percentage points, respectively.

Jie Zhao, Ziyu Jiang, Suhang Zheng +3

Alibaba Group Model · Logics-SWE-Qwen3.6-27B

Software Engineering AgentsAgentic RLMulti-Task RLOn-Policy Distillation
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Sep 19, 2026

Anatomy of a Closed-Loop Collapse: A Causal Case Study of a Compressed VLA Policy

Compressed manipulation policies can pass offline evaluation while failing in closed-loop execution; this dissociation is established in prior work and is not our claim. We contribute a causal anatomy of one naturally occurring case. An 8-layer distillation of Octo-Base retains 86% of parameters, passes every offline check we applied (0.996 and 1.000 teacher-ratios on the family's own validation metrics), and collapses in closed loop: 0/72 vs. the teacher's 40/72 on a simulated WidowX pick-and-place task. The collapse is structured, not diffuse: early task stages degrade gradually (the student moves the object at 90% of the teacher's rate and grasps at 55%), while transport-to-target fails categorically, at 0% in every training variant. Paired action-trace forensics isolate the signature: a negative, late-heavy zz residual, roughly 10x its post-repair magnitude, and persistent across the base distillation and both continuation branches. Four standard therapies fail under matched controls: continued training and in-domain offline data leave success at zero, even though the latter measurably improves marginal action statistics; command-level compensation recovers nothing at any offset, although the same perturbations degrade healthy policies; clamping the symptom in the command channel preserves grasping, yet success stays at floor. A minimal-pair intervention that substitutes half of the training stream with deployment-distribution teacher rollouts, with every other setting held fixed, restores parity with the teacher (18/36 vs. 17/36 held-out), eliminates that signature, and recovers a teacher-like perturbation-response profile. We claim existence, not universality. Operationally, offline gates, including a family's own validation metrics, are insufficient acceptance tests for compressed policies; a few dozen closed-loop trials sufficed to find what they missed.

Fengze Jia

The Ohio State University · The Ohio State University Columbus, OH, USA

Robotic Policy EvaluationVision-Language-Action ModelsRobotic ManipulationKnowledge DistillationOn-Policy Distillation
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Sep 18, 2026

Calibrating Teacher--Student Discrepancy for On-Policy Distillation

On-policy distillation (OPD) improves reasoning models by learning the token-level discrepancy between a stronger teacher and an on-policy student. However, this discrepancy does not purely reflect the capability gap between the teacher and the student: it also contains deviations arising from the teacher itself, which are consequently mixed into the observed teacher--student discrepancy and indiscriminately learned by standard OPD during training. This issue is further exacerbated by privileged OPD, where privileged information induces larger teacher-side likelihood shifts, thereby encouraging the student to learn more of the teacher's own deviation. We introduce Calibrated On-Policy Distillation (Cal-OPD), which estimates the teacher's self-deviation region through positive and negative privileged interventions and calibrates the original teacher--student discrepancy by retaining only the component that lies beyond this region. Experiments on mathematical reasoning benchmarks show that, while retaining only about 52--65% of the original teacher--student discrepancy as the optimization signal, Cal-OPD consistently outperforms standard OPD and its variants across model scales.

Qiangqiang He, Jin Li, MingCai Chen

State Key Laboratory for Novel Software Technology, Nanjing University, Nanjing, China · College of Software Engineering, Southeast University, Nanjing, China · Nanjing University of Posts and Telecommunications, Nanjing, China

On-Policy DistillationLanguage Model Distillation
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Sep 18, 2026

GVPO++: Group Variance Policy Optimization for LLM Post-Training and On-Policy Distillation

Post-training plays a pivotal role in enhancing the reasoning capabilities and task-specific expertise of large language models (LLMs). Despite recent advances in post-training methods, such as Group Relative Policy Optimization (GRPO), their practical deployment remains impeded by training instability arising from the reliance on importance sampling. We introduce Group Variance Policy Optimization (GVPO), a novel post-training method that integrates the analytical solution of KL-constrained reward maximization into its gradient weighting scheme. This formulation provides an intuitive interpretation: GVPO's gradient corresponds to the mean squared error between the central distance of implicit rewards and that of actual rewards. GVPO offers two key advantages: (1) it guarantees a unique optimal solution, exactly to the KL-constrained reward maximization objective, and (2) it enables flexible sampling distributions without requiring importance sampling. Beyond general post-training, we show that GVPO naturally extends to on-policy distillation (OPD). Furthermore, GVPO enables the optimization of a broad family of extended OPD objectives, providing a principled foundation for diverse objective design. By unifying theoretical guarantees with practical adaptability, GVPO establishes a new paradigm for reliable and versatile LLM post-training and on-policy distillation.

Kaichen Zhang, Yuzhong Hong, Junwei Bao +4

Policy OptimizationLLM Post-TrainingPolicy Gradient MethodsOn-Policy Distillation
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Sep 17, 2026

RetireOPD: Self-Retiring On-Policy Distillation for Agentic Reinforcement Learning

Multi-turn agents trained with reinforcement learning (RL) receive a single scalar reward per trajectory, which motivates self on-policy distillation (OPD) to supply dense token-level supervision from a self-teacher with privileged task skills, letting a skill-free student internalize them. This recipe, however, is undermined by two findings in agentic tasks: privileged information alone does not always make a teacher reliable, and the benefit of teacher supervision is stage-dependent. We therefore propose RetireOPD (Self-Retiring On-Policy Distillation), which first optimizes a decoupled, skill-conditioned teacher with environment rewards and then trains a skill-free student jointly with RL and OPD. Rather than following a predefined distillation schedule, RetireOPD adopts Adaptive Retirement: the student drops the teacher on its own once their discrepancy stops shrinking and it reaches a target fraction of the teacher's success rate, after which training proceeds with RL alone. Across Qwen2.5 models from 1.5B to 7B, RetireOPD improves ALFWorld success rate over RL baseline by 14.1% to 18.8% and WebShop accuracy by 11.8% to 19.0%, and surpasses its own skill-conditioned teacher in every setting.

Yan Yu, Zhengxi Lu, Yizhou Liu +7

Zhejiang University · Alibaba Group

Agentic RLOn-Policy DistillationRL for LLM Agents
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Sep 17, 2026

When EOS Tokens Disagree: Understanding Length Inflation in On-Policy Distillation

We study length inflation in on-policy distillation (OPD), where student responses can become excessively long and even exhaust the generation budget. We identify termination-token mismatch between base students and post-trained teachers as an important source of this behavior. Across Qwen3, Llama, and Gemma, the two models can place their stopping probability on different EOS tokens, even when their declared stopping sets are identical. This mismatch can suppress the student's preferred termination action without reliably transferring the teacher-preferred alternative. We show that aligning the decoding stopping set alone is insufficient, while treating functionally equivalent EOS tokens as a shared semantic stopping action substantially mitigates mismatch-induced length inflation across all three model families. To further understand how termination behavior evolves over training, we study OPD across different K2-Horizon training stages. This stage-wise analysis shows that termination preferences can shift substantially during training, while also revealing a distinct length inflation late in the OPD run that persists beyond termination alignment. Together, these results identify termination mismatch as an important, but not exhaustive, source of OPD length dynamics. We release an implementation incorporating the proposed termination-handling corrections.

Yuxiao Yang, Tianrun Yu, Shangzhe Li +6

University of North Carolina at Chapel Hill · Brigham Young University · Microsoft

Language Model DistillationOn-Policy Distillation
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Sep 16, 2026

Trajectory Learnability for Offline On-Policy Distillation with Imperfect Teachers

Offline on-policy distillation gains efficiency by collecting student trajectories and teacher supervision once and reusing them throughout optimization. The same reuse makes imperfect supervision persistent. Since even strong teachers can fail, we ask what remains learnable from imperfect teacher supervision? Teacher failure is only a coarse problem-level signal and does not imply that all supervision along the associated student trajectory is unhelpful. A natural alternative is to estimate teacher recoverability along the trajectory, but repeated continuations largely erase the efficiency advantage of offline distillation. We instead use teacher-successful problems to define a cheap reference for what the student can learn. We train on teacher-successful problems and measure how the likelihood of each observed token in trajectories from teacher-failed problems changes. We use these signed likelihood changes as an operational learnability signal: larger increases indicate behavior more strongly promoted by successful-only learning. We aggregate this signal into trajectory-level weights for the original distillation loss. Unlike continuation-based estimates, our learnability requires no additional generation and can be computed once from stored trajectories and model checkpoints. Across mathematical reasoning and code generation, our method improves an offline OPD baseline by up to 2.7 percentage points and matches or outperforms online OPD variants on multiple benchmarks. Despite the additional successful-only distillation stage, it uses 2 GPUs and about 22 GPU hours, compared with 3 GPUs and 36--48 GPU hours for representative online OPD methods.

Yihao Ai, Beibei Lin, Weilong Yan +1

National University of Singapore

Language Model DistillationOn-Policy Distillation
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Sep 15, 2026

Beyond Token-Local Imitation: Reward-Compatible Temporal Credit Assignment for On-Policy Distillation

On-policy distillation (OPD) has emerged as an effective approach for large language model post-training, yet existing objectives face a trade-off between objective fidelity and optimization stability. Token-level OPD provides stable but local supervision, whereas sequence-level OPD captures future credit at the cost of horizon-dependent variance. We establish a unified temporal-credit view of these formulations, showing that practical token-level OPD can be interpreted as a temporal approximation to the sequence-level reverse-KL gradient. Building on this connection, we propose γγOPD (GammaOPD), which uses discounted temporal credit assignment to balance long-horizon supervision and optimization stability, while admitting a horizon-independent variance bound. We further develop a reward-compatible bounded mixing (RBM) mechanism for γγOPD that balances verifiable outcome feedback with the discounted OPD advantage to move beyond purely teacher-dependent optimization. Experiments on mathematical and code reasoning demonstrate consistent improvements over existing OPD methods across vanilla, size-mismatched, and multi-teacher distillation settings.

Shiqi Liu, Zeyu He, Letian Tao +9

School of Vehicle and Mobility & College of AI, Tsinghua University · 2Didi Voyager Labs, DiDi Autonomous Driving

RL for Language Model ReasoningTemporal Credit AssignmentLanguage Model DistillationOn-Policy Distillation
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Sep 15, 2026

OPD-Aha: From Linguistic Momentum to Visual Reflection in Multimodal On-Policy Distillation

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.

Chenhao Qiu, Dawei Li, Yechao Zhang +2

Arizona State University · University of Virginia · Stevens Institute of Technology

Object Hallucination in VLMsMultimodal ReasoningOn-Policy Distillation
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Sep 14, 2026

Who Teaches Which Token? Verifier-Gated Multi-Expert On-Policy Distillation for Scientific Reasoning

Multi-teacher on-policy distillation (OPD) is becoming the standard way to integrate specialist capabilities into one model: train experts with RL, then distill them into the student on its own rollouts. Existing recipes assign supervision at the sequence level - each prompt goes to one domain teacher and every token receives the same weight - which implicitly assumes that a teacher is uniformly useful across a response. We find instead that useful teacher signal is sparse and heterogeneous along a reasoning trajectory, which raises a finer question: who should teach which token? Verifier-Gated Multi-Expert On-Policy Distillation (VG-OPD) answers it by verification: the counterfactual gain of an expert on a specific answer criterion licenses that expert to teach, its disagreement with the student localizes the supervision, and criterion importance sets its weight; the gated KL enters GRPO as an additive token-level advantage. Instantiated for scientific reasoning with RL-trained capability experts, VG-OPD attains the best overall performance on seven benchmarks for 4B and 8B students, ranking first on five at both scales, with the largest gains on knowledge-intensive scientific reasoning tasks. Further analysis shows that the gains come from localizing verified supervision rather than from adding teachers or distillation loss: misplacing the same supervision budget is the single most damaging change, and indiscriminate distillation drags RL below its own floor where gated distillation lifts it.

Xun Xu, Zaixi Zhang

1Fudan University · 2Hong Kong University of Science and Technology

RL for Language Model ReasoningMulti-Teacher Knowledge DistillationOn-Policy DistillationScientific Reasoning in Language ModelsKnowledge Distillation
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Sep 14, 2026

Reducing the Output-Mode Gap in Speech Language Models via Joint-Output On-Policy Distillation

Autoregressive generation of interleaved text and acoustic tokens is a common approach to spoken-response generation in speech large language models. Although this design enables streaming generation with explicit textual guidance, generated acoustic tokens become part of the context for subsequent text predictions. Given identical speech inputs, we observe markedly lower answer accuracy for the internal text generated in speech-to-text-and-speech (S2TS) mode than for speech-to-text (S2T) responses. We term this discrepancy the output-mode gap (OMG). To reduce OMG, we propose Joint-Output On-Policy Distillation (JO-OPD), which distills the model's stronger S2T policy into joint generation using student-generated S2TS trajectories. At each text position, the S2T teacher provides soft targets from a text-only projection of the student's preceding outputs, while the student predicts from the corresponding full interleaved history. A preservation objective further regularizes native non-text predictions. Experiments on Step-Audio-2-mini and Baichuan-Audio-Instruct reveal OMG across two interleaved generation architectures. On Step-Audio-2-mini, JO-OPD reduces OMG from 42.87 to 16.26 percentage points on Spoken-MQA and from 29.72 to 13.04 points on speech-rendered GSM8K, with little change in S2T accuracy and substantially larger reductions than matched SFT baselines. ASR-based evaluation further shows a 7.49-point improvement in spoken-answer accuracy on Spoken-MQA.

Daxin Tan, Dehua Tao, Chengxi Deng +2

AI Lab, Leibniz Research Center, Huawei · The Chinese University of Hong Kong · City University of Hong Kong

On-Policy DistillationSpeech Language ModelsSpoken QA
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Sep 13, 2026

Know When to Stop, Where to Restart: Accelerating Multi-Turn Agentic On-Policy Distillation

On-policy distillation (OPD) has become a standard approach for transferring capabilities from large teachers to compact students. Its cost, however, is dominated by autoregressive student rollouts and scales poorly in multi-turn agentic settings. Existing acceleration methods truncate or relocate the supervision signal according to fixed, offline budgets, despite substantial variation in teacher-signal reliability both within and across trajectories. Our empirical analysis on τ2τ^2-bench reveals a clear structure in this variation: informative supervision is concentrated in the prefix of each turn, and, most importantly for multi-turn agentic training, the cross-turn loss of teacher endorsement is temporally locked to the student's first erroneous action rather than accumulating gradually over turns. Building on these findings, we propose STRIDE (Stop-and-Restart on-policy Distillation acceleration), which combines two complementary techniques: adaptive early stopping, which terminates a rollout once the cumulative teacher log-probability falls below an out-of-distribution threshold, and a prefix buffer, which caches high-quality prefixes and restarts generation at the weakest correct turn. Together, these mechanisms induce a data-driven curriculum that progressively extends coverage to later turns. On τ2τ^2-bench retail, our method matches full-trajectory OPD and exceeds the 30B teacher at a 3.73×3.73\times speedup, surpasses the baseline itself at 2.34×2.34\times, and retains a 4.51×4.51\times speedup under cross-domain multi-teacher training. As a supplementary generalization test beyond the agentic setting, STRIDE outperforms full OPD on AIME 2025 at a 5.10×5.10\times speedup and on AIME 2024 at a 3.08×3.08\times speedup; averaged across the two evaluations, both fixed-budget truncation baselines remain below full OPD.

Zhiyu Gui, Kexin Huang, Jia Guo +6

University of Science and Technology of China · Ant Group

On-Policy Distillation
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Sep 12, 2026

Data-Free On-Policy Distillation: How Far Can We Go Without External Data?

On-policy distillation (OPD) is increasingly applied to frontier foundation model post-training. Prior work in this area has largely focused on algorithmic advances, yet it remains unclear how much OPD depends on its training questions and, in particular, how far this dependence can be reduced. Across two representative single-teacher OPD settings, we find that training on 8 real prompts yields performance comparable to training on 17k problems, while datasets differing substantially in measured difficulty and initial distillation gap yield similar outcomes. Our analyses suggest two complementary explanations: repeated sampling could allow even a few prompts to expose substantial teacher supervision, while OPD transfers generalizable reasoning capabilities beyond dataset-specific knowledge. Building on these observations, we next propose a data-free on-policy distillation (DF-OPD) setting to investigate whether the system can supply the training questions itself, eliminating the need for external data. With 64 self-generated questions obtained without seed examples, DF-OPD yields performance comparable to full-data OPD in both single-teacher settings. This finding also holds in multi-teacher OPD: across mathematics, code, and instruction following, 1k generated questions achieve performance comparable to training on approximately 7k real post-training examples. We further explore whether OPD can operate even without explicit training questions. The experiments show that this is effective only in limited cases, where the student unexpectedly generates and answers its own questions, thereby reducing the process to an implicit form of DF-OPD. Together, these findings invite a reassessment of the role of training data in on-policy distillation. Code is available at https://github.com/Ryuki661/DF-OPD

Gengsheng Li, Mao Zheng, Mingyang Song +10

Foundation Model Research Center, Institute of Automation, Chinese Academy of Sciences · School of Artificial Intelligence, University of Chinese Academy of Sciences · Foundation Model Department, Tencent +2

On-Policy DistillationKnowledge DistillationData-Free Knowledge DistillationSynthetic Data Generation
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Sep 10, 2026

A Unified Per-Token Gating Family for On-Policy Distillation: FKL/RKL Mixing with Multi-Channel and Bias Coefficients

Per-token gating of forward/reverse KL losses has become a standard technique for on-policy knowledge distillation (OPD), but existing methods such as EOPD (Jin et al., 2026) and ToDi (Jung et al., 2025) each fix a single gating signal and a single gating direction, and the two have never been compared directly. We introduce a four-coefficient parameterization lambda_t = sigma(a * h_t + b * u(x) + c + d * gap_t) in which direction-aligned proxies of EOPD and ToDi appear as one-dimensional (1D) restrictions, and which adds multi-channel composition and an explicit bias as further degrees of freedom. On TweetEval (Barbieri et al., 2020) emotion and hate, with a Qwen3-32B teacher and a Qwen3-4B student, configurations in the full family reach higher accuracy than the matched-magnitude single-channel (entropy-only / gap-only) 1D restrictions in 33 of 36 comparable cells, and a 26-cell mean-match isolation experiment places dynamic gating ahead of effective-KL-matched static baselines in 19 of 26 cells. Because cells share training data, models, and parameter substructure, we report both counts as exploratory aggregate directional evidence rather than as independent hypothesis tests. Targeted three-seed paired replications of the nine headline comparisons singled out by that sweep -- including a third task, offensive -- are directionally consistent, but individually smaller than the single-seed estimates and not significant at n=3. We therefore present the parameterization primarily as a shared coordinate system for comparing per-token gating designs in short-output classification OPD.

Suwan Wu, Yumeng Lin, Pengcheng Yuan +1

Xiaohongshu Inc. · Tianjin University

Adaptive Loss WeightingLanguage Model DistillationOn-Policy Distillation
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Sep 10, 2026

KuaiRP Series Role-playing Models Technical Report

This paper introduces the complete technical solution for the KuaiRP series of role-playing models. We aim to achieve four core objectives for a dedicated role-playing model: simplified prompt engineering, highly stable output quality, built-in domain world knowledge, and high-efficiency deployment with a small parameter size. However, effectively injecting deep domain knowledge often leads to a severe catastrophic forgetting of the model's general agent capabilities. To overcome this trade-off, we propose a multi-stage training pipeline. First, we design a standardized character template and construct an SFT data pipeline based on user behavior simulation and reverse profile filtering. Next, we utilize a rule-based composite reward function during the Reinforcement Learning (RL) phase to eliminate common degradation phenomena like length expansion and repetitive generation. Finally, to recover the general capabilities compromised during SFT and RL, we propose a novel self-distillation paradigm using Two-stage On-Policy Distillation (OPD) equipped with Cumulative-Divergence Decay (CDD). By using the domain-adapted model as the teacher and the original base model as the student, we effectively balance deep domain knowledge injection with the preservation of general agent capabilities. Experimental results demonstrate that the KuaiRP models not only match the current state-of-the-art proprietary models in role-playing fidelity within our target domains, but also successfully recover general agent capabilities, maintaining extremely low deployment costs.

Yipeng Wang, Ziwei Zhang, Jiahui Zhang +2

Kuaishou GameMind Lab

Large Language Model-Based Role-Play SimulationKnowledge Augmentation for Language ModelsOn-Policy DistillationCatastrophic Forgetting
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Sep 9, 2026

On-Policy Distillation for Vision-Language Model Adaptation, an Effective Paradigm on Low-Quality Multimodal Data

Knowledge distillation offers an efficient route to transfer a task-adapted vision-language teacher to a compact student. The training target in current vision-language distillation methods is typically constructed from the teacher prediction and applied uniformly to all training samples, making it unreliable under class and domain shifts. In this paper, we argue that distillation target construction should be treated as a dynamic training decision rather than a fixed recipe. To this end, we propose OnPoKD, an on-policy distillation framework for vision-language model adaptation. To the best of our knowledge, OnPoKD is the first framework that applies on-policy distillation to vision-language model adaptation by learning target construction as a policy decision. OnPoKD learns a lightweight controller that constructs sample-wise adaptive targets using reliability and disagreement cues from the teacher model, student model, and zero-shot prior. Instead of relying on a fixed teacher prediction, the controller dynamically balances teacher supervision, zero-shot prior guidance, and hard-label anchoring through bounded policy actions, allowing the distillation target to adapt to varying sample reliability and training stages. The policy controller is updated with validation feedback, encouraging target construction to optimize transferability rather than merely fitting the training distribution. Since the controller is only used during training, OnPoKD can be seamlessly integrated into existing vision-language distillation pipelines while preserving the original inference architecture and test-time cost. Extensive experiments on Base-to-novel generalization and Cross-dataset transfer benchmarks show that OnPoKD consistently improves over strong vision-language distillation baselines.

Hongyuan Zhang, Xianda Guo, Yanlun Peng +6

The University of Hong Kong, Hong Kong SAR, China · Great Wall Motor, China · School of Information Science and Technology, University of Science and Technology of China, China +4

VLM AdaptationVLM DistillationOn-Policy Distillation
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Sep 9, 2026

CompassOPD: Cross-Family On-Policy Distillation via Within-Family Likelihood Shifts

On-policy distillation (OPD) provides dense token-level supervision on student-generated trajectories. Although OPD performs strongly when teacher and student belong to the same model family, we find that its effectiveness degrades in cross-family settings even after tokenizer alignment, with substantially stronger external teachers offering little additional improvement. To understand this disconnect, we decompose the cross-family OPD signal into two components: an offset between a low-capability teacher-family reference and the student, and the within-family log-likelihood shift from that reference to the strong teacher. Standard OPD transfers both components together, allowing the offset to dominate the update direction and obscure the changes associated with teacher capability improvements. We propose CompassOPD, which removes this offset and transfers the within-family shift, while a frozen student reference anchors updates to the student's initial policy. Thus, both teacher-side and student-side changes are measured within their respective model families. Experiments across three student families and multiple teacher families show that CompassOPD consistently outperforms standard cross-family OPD, improving average reasoning accuracy by up to 5.50 points. For an MoE teacher, we further construct the reference directly from the teacher checkpoint by reducing expert activation, eliminating the need for a separate reference checkpoint while retaining a 3.43-point gain over OPD.

Naibin Gu, Qingyi Si, Chenxu Yang +5

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

Language Model DistillationOn-Policy DistillationLLM Reasoning
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Sep 8, 2026

Eliciting Weak-to-Strong Generalization with On-Policy Reverse Distillation

Weak-to-strong generalization asks whether stronger models can learn from weaker supervisors and surpass them. This is particularly important for successive model generations and multi-domain consolidation, where frontier-scale post-training from scratch can be prohibitively expensive. Yet conventional distillation treats the weak teacher as an optimization target, potentially imposing its capacity ceiling on the student. We introduce On-Policy Reverse Distillation (OPRD), which evaluates the teacher's policy shift relative to its reference policy on student rollouts and amplifies the component of the student's verifier-driven policy gradient along that direction. By rescaling only verifier-supported updates, OPRD preserves the stationary points of policy optimization while accelerating learning beyond the teacher. Our evaluations cover mathematical reasoning, logical reasoning, code generation, and visual tool use. In both successive model transfer and multi-teacher distillation, OPRD achieves higher performance with fewer student updates than existing RL and distillation approaches. Response-style analysis shows that OPRD students remain closer to verifier-only RL models than to their weak teachers, suggesting that guidance accelerates rather than redirects student optimization. Strong-to-weak results further show that OPRD combines verifier-driven optimization with teacher guidance regardless of capacity ordering.

Youngrok Park, Sangmin Bae, Hojung Jung +6

KAIST AI · Microsoft · University of Toronto +3

Policy GradientWeak-to-Strong GeneralizationMulti-Teacher Knowledge DistillationOn-Policy DistillationRL Post-Training
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Sep 8, 2026

TV-Regulated OPD: Direction Matters in On-Policy Distillation

On-Policy Distillation (OPD) facilitates the transfer of knowledge from domain expert to student in the post-training phase of Large Language Models (LLMs). However, the supervision signals in mainstream OPD methods suffer from high variance and noise which is generally instable during training. In this work, we systematically investigated what really matters to the performance and the fundamental mechanisms behind the instability during training. We found that retaining only the sign of token-level advantages is sufficient to achieve the performance comparable to standard OPD. Meanwhile, smoother and bounded advantages can stabilize the training process without sacrificing its performance. These motivated us to shape the advantages using the Total Variation (TV) and propose a robust TV regulated On-Policy Distillation (TV-OPD) method. Benefiting from the bounded and diminished advantages, TV-OPD exhibits stable training dynamics and steady late-stage performance. We conducted comprehensive experiments and found that, across various settings, TV-OPD consistently achieved better performance and lower variance in the late-stage of training.

Han Xiao, Yifan Niu, Dongyi Liu +2

The Hong Kong University of Science and Technology (Guangzhou) · The University of Edinburgh · The Hong Kong University of Science and Technology

Preference OptimizationOn-Policy DistillationRL Post-TrainingTV Regularization
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Sep 8, 2026

Distillation as Probability Transport: Routed On-Policy Distillation

On-policy distillation (OPD) transfers teacher knowledge on student-generated trajectories, but efficient sampled objectives reduce the teacher distribution to scalar credit on individual tokens. Such credit indicates whether a token should gain or lose probability, yet leaves the corresponding redistribution unspecified. We recast OPD as teacher-guided probability transport and propose RouteOPD (Routed On-Policy Distillation), which decomposes local teacher--student disagreement into student-excess sources and teacher-deficit destinations and couples them into explicit transport pairs. RouteOPD optimizes pairwise log-odds toward jointly realizable targets obtained from a bounded teacher potential, while adapting the transport budget to the concentration of teacher demand. This formulation directs updates toward teacher-preferred destinations and controls their magnitude within a single transport operator. Experiments across four teacher--student settings and four mathematical-reasoning benchmarks demonstrate that RouteOPD consistently outperforms sampled reverse-KL OPD, with improvements accompanied by higher routing fidelity and lower background leakage. These results demonstrate the effectiveness of explicitly modeling probability transport in on-policy distillation.

Tianle Xia, Lingxiang Hu, Yiding Sun +6

Tencent

Language Model DistillationOn-Policy DistillationOptimal Transport
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