On-Policy Distillation

We study empirical scaling properties for text conditioning in visual generation. Such properties have rarely been measured because diffusion loss does not scale with the number of tokens in natural-language prompts. Surprisingly, we find that the converged diffusion loss scales with the amount of structured language in the prompt. To quantify structured language, we adapt two complementary measures: a white-box likelihood metric (GPG) and a black-box attribute metric (ED). Across controlled training runs, the converged diffusion loss decreases approximately linearly with GPG and follows a power law with ED. Guided by these scaling properties, we improve \emph{diffusability} by constructing structured prompts with semantic and geometric annotations derived from images, and improve \emph{promptability} by training a prompter through supervised fine-tuning, cold-start, and verifier-gated on-policy distillation. The resulting system outperforms all evaluated open-weight models on nearly every compositional, reasoning, and world-knowledge benchmark, while matching or surpassing the strongest closed-weight models on most evaluations.

On-policy distillation (OPD) provides dense teacher supervision along student-generated trajectories, but its online rollout process incurs substantial computational cost, particularly when a few long responses delay batch completion. Existing acceleration methods typically control rollout length using fixed budgets or absolute teacher--student agreement thresholds, which may not reflect learning progress across different models and training stages. We propose Adaptive FastOPD, a progress-aware strategy that expands the rollout horizon only when learning near the current boundary region has plateaued and the current horizon is sufficiently utilized. The former is determined from four teacher--student signals measured relative to their values upon entering each horizon, making expansion responsive to stage-specific progress rather than a predefined step interval or an absolute threshold on the raw agreement signals, while the latter prevents a small number of long responses from triggering increases in rollout cost. Across two teacher--student pairs, Adaptive FastOPD achieves the highest average performance while reducing training time by 49.1--71.2% relative to OPD 15K, and remains robust across a range of hyperparameter settings.

Graphical user interface (GUI) agents based on large language models are increasingly deployed across mobile, web, and desktop environments. However, existing agents are typically domain-specific, limiting the deployment and user experience. This motivates the consolidation of specialized models into a single cross-environment policy. Weight merging directly merges domain-specific experts but can corrupt executable actions under expert disagreement, while on-policy distillation (OPD) avoids conflicting teacher supervision yet still treats all response tokens equally during distillation, ignoring that action tokens are the only interface between the environment and the agent. To address this, We introduce MAGA that re-allocates training signal according to the structured action. Based on the correctness of the generated action, it suppresses unnecessary or invalid distillation signals and focuses learning on erroneous actions. Besides, a training-only hint optimizes the supervision signal provided by domain-specific teachers without changing the student input. Across two model scales, MAGA achieves the highest mean success rate, outperforming the strongest baseline by 2.0% at 8B and achieves almost the same average performance with teachers.

Reinforcement learning with verifiable rewards (RLVR) broadcasts a single response-level reward to every token, while on-policy distillation (OPD) scores each token against a stronger teacher for a dense advantage but caps performance at teacher quality and discourages exploration beyond it. Their complementarity makes combining RLVR and OPD promising, but we find that fusing the two advantages with a fixed coefficient triggers entropy collapse from two miscalibrations: a magnitude mismatch, where token-level OPD advantages can spike far beyond the bounded RLVR advantage and erase its signal, and a temporal mismatch, where sustained full-strength OPD keeps pulling the student toward the teacher and limits exploration needed to surpass it. We propose SAF, a Stable Advantage Fusion framework that resolves both issues via a lightweight, four-stage pipeline applied only to the OPD advantage: a sparsify-then-compress mechanism for magnitude control paired with a warm-up-then-anneal mechanism for temporal control, with each stage independently switchable and adding negligible overhead. Instantiating RLVR with GRPO, we evaluate SAF across seven mathematical reasoning and code generation benchmarks with Qwen3-1.7B/4B/8B: SAF avoids entropy collapse and consistently outperforms fixed-coefficient GRPO+OPD fusion, improving the aggregate score by 0.51-2.70% across all six model-domain settings while achieving more stable training.

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

On-policy distillation (OPD) provides dense token-level supervision from a teacher, but its effectiveness can depend on teacher consistency, meaning that the model providing OPD supervision should also have generated the demonstrations used to train the supervised fine-tuning (SFT) reference. However, this condition is frequently violated in practice when SFT data have mixed or unknown provenance or when different models are preferred for SFT data generation and subsequent distillation. In such cross-teacher settings, even a stronger OPD teacher can yield little improvement over the SFT reference. We find that raw teacher--reference disagreement contains potentially useful context-specific teacher evidence as well as a recurring component associated with differences in wording, formatting, and reasoning cadence. We introduce Lightning OPD 2.0 with cross-fitted style residualization, which uses rollout-level cross-fitting to estimate this recurring component as an operational proxy for style-token bias and subtracts it before constructing the token-level OPD update. Across mathematical reasoning and code generation benchmarks, Lightning OPD 2.0 consistently outperforms Lightning OPD in cross-teacher settings. Starting from Klear-Reasoner-8B-SFT, Lightning OPD 2.0 reaches 82.4% on AIME 2024 and 63.0% on LiveCodeBench v5. Together, these results establish Lightning OPD 2.0 as a practical approach to cross-teacher OPD, relaxing teacher consistency as a prerequisite and allowing the SFT data generator and distillation teacher to be selected independently. Code will be released soon.

Interleaved multimodal Chain-of-Thought (CoT) improves visual reasoning by incorporating auxiliary visual evidence into intermediate reasoning. However, existing approaches remain constrained by externally defined reasoning traces and visual operations, limiting their ability to develop flexible and abstract visual thinking. Reasoning with latent has recently offered a promising direction by internalizing intermediate computation into continuous representations. Nevertheless, existing visual-latent methods mainly supervise latent states through alignment with compressed auxiliary visual features, treating them as proxies for visual observations rather than active reasoning states. Consequently, they capture the provided evidence but fail to fully internalize the abstract reasoning process induced by multimodal CoT. In this paper, we propose OPLD (On-Policy Latent Distillation), a simple framework that transfers the reasoning capability induced by privileged multimodal CoT into latent reasoning representations. Extensive experiments on diverse multimodal benchmarks demonstrate that OPLD consistently outperforms existing latent reasoning methods and achieves state-of-the-art performance on multiple benchmarks. The results suggest that supervising latent representations at the reasoning-process level provides a more effective paradigm for multimodal latent reasoning than conventional feature-level alignment.

Large language model training in open-ended domains lacks verifiable rewards, making task preferences difficult to formalize as effective supervision. Contexts can convey such preferences, yet provide little additional supervision once distilled into the student, motivating contexts that evolve with student performance. However, directly using evolving contexts as in-training supervision results in an unstable distillation target and conflicting distributions, requiring mechanisms to stabilize target and downweight conflicts. In this paper, we analyze the effect of contexts through a decomposition of the reverse KL objective, revealing two findings: the student is distilled toward the geometric mean of context-conditioned teachers, and the objective contains a conflict term that measures conflicts among these teachers. Based on this decomposition, we propose Flux-OPD, an OPD paradigm that uses evolving contexts as in-training supervision to capture task preferences in open-ended domains. Flux-OPD treats the differences between context-conditioned and context-free teachers as contextual difference signals, injects them as contextual corrections into the context-free teacher anchor, and weights their correction strength using the conflict term as an indicator. Experiments on open-ended tasks show that Flux-OPD outperforms existing OPD paradigms, highlighting the potential to combine teacher supervision with evolving contexts.

A single reinforcement-learning run can produce a strong reasoner yet an incomplete teacher: it often amplifies only a subset of the valid solution modes. We argue that reinforcement learning (RL)-trained policies should therefore be viewed as local probes of a multi-basin reasoning solution manifold, rather than as globally reliable supervisors. Based on this view, we propose an expand-then-compress framework that couples teacher construction with multi-teacher policy distillation. In the expansion stage, Residual Group Relative Policy Optimization (RGRPO) trains a sequence of teachers from a common initialization and redirects each later round toward examples not yet covered by the accumulated teacher union. In the compression stage, reliability-gated Teacher-Union On-policy Distillation (TU-OPD) lets the student learn from its own response prefixes. For each example, only reliable teachers contribute, and their sampled-token OPD losses are weighted by their per-example quality. We further introduce Consensus-Residual Decomposition, which preserves a winner teacher's excess token preferences over its reliable peers, preventing specialist behavior from being suppressed during teacher aggregation. Experiments on mathematical reasoning, code generation, and instruction following show that the resulting Qwen3-1.7B student consistently outperforms the strongest individual teacher across all three domains, yielding relative improvements of 2.0%, 8.3%, and 6.9%, respectively, while retaining single-model inference. These results establish a simple but powerful principle: stronger students can be obtained not by selecting a single better teacher, but by deliberately constructing and compressing a complementary teacher union.

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

Fine-tuning is the dominant paradigm for specializing large language models (LLMs), yet it exposes a critical vulnerability: malicious data providers can embed harmful behaviors into downstream corpora, creating models that retain professional skills while violating human values on demand. Existing safety-realignment defenses often fail in practice due to three key limitations: they frequently cause catastrophic forgetting of specialized skills; their effectiveness collapses when the defender cannot observe the attacker's prompt template; and successfully realigned models remain susceptible to re-jailbreaking via simple system prompt switches. To address these challenges, we propose Routing-based On-Policy Distillation (ROPD), a novel realignment framework that models the divergence between aligned and compromised output probability distributions rather than fitting specific prompt templates. We conduct extensive experiments comparing ROPD against four state-of-the-art baselines across three datasets and three base models with varying alignment strengths. Our results demonstrate that when baseline defenses face template mismatches, often accompanied by severe degradation in downstream task performance. In contrast, ROPD substantially mitigates template-mismatch risks, maintaining superior robustness in both defense effectiveness and capability preservation. While our analysis indicates ROPD is not entirely immune to template shifts, its performance degradation is negligible compared to existing methods, establishing a new standard for robust LLM realignment.

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

On-policy distillation (OPD) grounds token-level supervision in the student's own trajectory, yet suffers from prefix failure: once the student commits to a wrong reasoning direction, all subsequent generation builds on this deviation, producing misdirected continuations that elicit unreliable supervision and waste compute. We identify a teacher-student continuation asymmetry on failed prefixes, where the teacher tends to redirect while the student continues along the original direction, and convert it into a label-free handoff trigger in Relay On-Policy Distillation (Relay-OPD). During training, Relay-OPD constructs relay trajectories by letting the teacher briefly take over at detected trigger points to produce a teacher leg, after which the student resumes and is optimized on the resulting trajectory. A limited relay budget concentrates intervention on critical early positions while limiting departure from the student policy. With a Qwen3-4B-Instruct-2507 teacher and Qwen3-0.6B/1.7B-Non-Thinking students on eight mathematical reasoning benchmarks, Relay-OPD achieves the best or second-best results on every benchmark, outperforming standard OPD by +5.73% and the strongest baseline FastOPD by +1.49% on average for 1.7B, with consistent gains at 0.6B. Training trajectory length is reduced by over 50%.

On-policy distillation (OPD) adapts diffusion models by querying a teacher along trajectories generated by the current student, but how it should behave under classifier-free guidance (CFG), a default component of modern diffusion systems, remains poorly understood. Existing OPD methods naturally extend velocity matching to the CFG-composed prediction, directly matching teacher and student guided velocities. We show that this objective is under-identified at the branch level: positive- and negative-branch errors can compensate in the guided prediction. Through two contrasting cases, we find that naive matching remains effective under shared negative conditioning, where both branch errors decrease jointly. When the model's native CFG schema retains privileged information in the teacher's negative branch that is unavailable to the student, however, this joint reduction breaks down and the composed objective induces antagonistic branch-error dynamics, reducing the positive-branch error while increasing the negative-branch error. We term this failure mode Negative Branch Asymmetry (NBA). To address NBA, we introduce Positive--Direction Matching (PDM), a branch-aware OPD objective that separately constrains the positive prediction and the CFG conditional direction. We apply PDM to dense-to-sparse video control, where naive guided matching is highly sensitive to inference guidance scales, while branch-aware supervision enables more robust and effective knowledge transfer.

Multi-turn long-horizon planning is critical for foundation model agents, yet how to fundamentally improve it remains unclear. Existing models are trained on uncontrollable and opaque Internet data, making it difficult to identify how planning ability is acquired, shaped, and integrated. To address this challenge, we introduce a unified and controlled multi-turn environment that enables precise control. It allows systematically study long-horizon planning across three stages. (1) Planning ability acquisition during pre-training. We study data format, distribution, and quality. Explicit world model construction through CoT state transition modeling yields stronger long-horizon generalization. Atomic skills alone are insufficient for compositional generalization, whereas a litte long-horizon data works. Moreover, suboptimal trajectories severely impair performance because errors amplify over long horizons. (2) Planning ability shaping via GRPO and OPD post-training. Through mutual information, we distinguish general planning patterns from task-specific planning knowledge. For planning patterns, we identify three application regions of post-training: unnecessary, effective, and unsupported. OPD has a broader effective region than GRPO under low-quality and long-horizon settings, as it provides more consistent update directions. For planning knowledge, distilling unseen procedures from a teacher with different knowledge may impair student's prior world modeling without fully establishing new knowledge. (3) Planning ability integration through MOPD post-training. We show that multi-teacher on-policy distillation (MOPD) integrates capabilities by converging to shared planning-pattern across environments. Compatible patterns enable cross-environment generalization, partially shared patterns support continual learning, while completely conflicting patterns cause severe interference.

While on-policy distillation (OPD) effectively addresses sparse rewards and exposure bias in large language model post-training, its extension to flow models remains underexplored. To this end, we propose Flow Continuous Trajectory Supervision (FlowCTS), which matches subsequent student and reference trajectories initialized from the same student-visited state. Using the integral relation between trajectories and velocity fields, we derive a temporally weighted velocity-matching upper bound and discretize it into practical objectives parameterized by the number of supervision steps. Under a multi-reference setup, single-state FlowCTS-OPD outperforms vanilla KL-based OPD with faster convergence. FlowCTS-OPD improves GenEval from 0.90 to 0.93, OCR from 0.90 to 0.92, and PickScore from 22.75 to 23.06, while outperforming a mixed-reward RL baseline across all target metrics. Further analysis reveals a clear temporal supervision mismatch in vanilla KL-based OPD arising from its auxiliary SDE transition kernels. Beyond on-policy setting,FlowCTS also consistently outperforms vanilla SFT , particularly on OCR, while increasing supervision steps exhibit a trade-off between richer trajectory information and greater optimization difficulty.

On-policy distillation (OPD) trains a student on its own trajectories while a teacher supplies dense token-level likelihoods at student-visited prefixes. These likelihoods are often read locally: agreement appears safe to imitate, whereas disagreement appears to identify an error. We show that both readings are confounded by the outcome of the completed trajectory. We introduce an outcome-resolved diagnostic that crosses pointwise teacher-student divergence with final-answer correctness, separating safe imitation, productive divergence, harmful divergence, and agreement-on-failure. In an eight-seed mathematical-reasoning study with a Qwen3-8B student and Qwen3-32B teacher, agreement-on-failure constitutes 67.84% of pooled response-token mass; with a Qwen2.5-7B/32B pair it remains 67.68%. The result persists across threshold, sequence-level, format, and truncation audits. Even on prompts that the Qwen3 teacher solves in all four independent attempts, student accuracy rises to 86.91% but agreement-on-failure remains 14.76%. We then run three matched training probes that use the available signals to imitate, mask, or contrast whole trajectories; none consistently reduces agreement-on-failure. The result points to a localization limitation: local divergence paired with a trajectory-level outcome does not identify where a failed trajectory became unrecoverable. Addressing this limitation requires additional positional information, such as process labels, teacher continuations from student prefixes, or token-level alignment across rollouts. Our contribution is therefore diagnostic rather than a new training method.

Open-weight language models from different families exhibit complementary capabilities, motivating their consolidation into a compact student through on-policy distillation (OPD). However, full-vocabulary OPD typically assumes a shared tokenizer, while existing cross-tokenizer methods may discard teacher probability mass or assign it to student tokens with unrelated content. We introduce Byte-Prefix Marginalization (BPM), which re-expresses the teacher's next-token distribution over the student vocabulary in a shared byte space. Specifically, BPM assigns each teacher token's probability to the longest student token whose byte representation is a prefix of the teacher token's bytes, aggregates mass mapped to the same student token, and places otherwise unmatched mass in an explicit residual category. This produces a vocabulary-complete, byte-aligned, and mass-preserving target for dense OPD. The target exactly recovers the teacher-induced byte-prefix marginal when the relevant prefix does not span multiple teacher tokens (a condition satisfied at more than 99% of training positions) and uses a mass-preserving, chain-factorized lower bound otherwise. Across Qwen3-32B, GLM-Z1-9B-0414, and MiniMax-M2.7 as teachers, BPM consistently outperforms current cross-tokenizer methods on six mathematics and programming benchmarks, improving six-benchmark avg@8 by 3.7-6.6 points over the strongest baselines.

Omni-modal models provide a unified interface for text, images, and audio. However, improving these abilities together remains difficult, as post-training on pooled multimodal data often fails to preserve the strengths of modality teachers. On-policy distillation (OPD) has recently become popular in model post-training. It samples responses from the current student and compares the teacher's and student's next-token distributions along those responses, yielding dense supervision while reducing the mismatch between training and inference. Despite these advantages, standard OPD does not readily extend to several modality teachers. Their guidance may favor conflicting changes to the shared model, while matching each teacher's next-token distribution can prevent the student from moving beyond that teacher. To address these challenges, we propose On-Policy Omni Distillation (OPOD), which consolidates text, image, and audio teachers into one omni model. OPOD routes each response to the corresponding teacher, controls the teachers independently, and applies guidance only when the teacher assigns a higher probability to the generated token. The selected teacher also evaluates answer confidence and whether the reasoning increases support for the answer. Extensive experiments on twelve benchmarks show that OPOD achieves the best average at three model scales, reaching 70.8, 51.7, and 46.2 and outperforming the strongest comparator by 2.1, 1.8, and 1.7 points. At 30B, it surpasses the base model and pooled RL training on all twelve benchmarks, and ranks first or second on eleven even when the teachers are included. Only the student is retained for deployment.

Vision-language models have shown strong potential for social robot navigation by leveraging rich semantic understanding of complex environments and human behaviors. However, large scale VLMs are difficult to deploy on resource-constrained robotic platforms, while lightweight VLMs often lack sufficient social reasoning capability. To address this problem, we propose SOPD-SocialNav, a selective on-policy distillation (SOPD) method that transfers social navigation knowledge from a large teacher VLM to a lightweight student VLM. SOPD introduces an entropy-based token selection mechanism that uses teacher uncertainty to identify socially informative decision tokens, while suppressing gradients from low-entropy tokens corresponding to trivial navigation states. A temperature-controlled Jensen-Shannon divergence objective is then used to align the student and teacher distributions on the selected tokens. Experiments on the SNEI and MUSON benchmarks demonstrate that SOPD consistently outperforms supervised fine-tuning, off-policy distillation, and standard on-policy distillation baselines in action prediction, perception consistency, and reasoning consistency. Real-world deployment on a Scout Mini robot further shows that the distilled model can generate more socially appropriate navigation behaviors in conversational and queuing scenarios. These results suggest that SOPD is an effective strategy for building lightweight yet socially aware VLM-based navigation systems.

Large-scale online reinforcement learning (RL) is the predominant means of eliciting advanced abilities including long-term reasoning and agentic tool use in large language models (LLMs). However, continuing to scale it across vast task domains of interest remains challenging in both computational infrastructure and cost, especially when considering RL as merely a one-off learning stage. Recently, a widely used technique for distilling knowledge across various domains and training stages, multi-teacher on-policy distillation (MOPD), helps to decouple the RL stage, saving costs, while maintaining generality across vast domains. Nonetheless, similar to online RL, MOPD requires coupled inference and backward passes, which continues to limit its scalability and computational efficiency. To address these challenges, we propose REGEN: Replay-recycling for Expert-to-Generalist Distillation with Offline RL. Instead of distilling from multiple teacher models, REGEN trains a generalist by simply recycling the replay memory -- the free by-product of the teachers' specialized RL training -- and employing offline RL algorithms. REGEN completely decouples the rollout sampling from the backward training process and thus greatly reduces the training cost. Across mathematical reasoning, code generation, and instruction following, REGEN matches the accuracy of MOPD at substantially lower cost. It potentially turns online RL into a data synthesis process instead of a one-off learning stage, and can be extended to large-scale post-training without requiring heavy computational load. Code is available at https://github.com/yunjie-sysu/REGEN.

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

Antibodies are essential therapeutic molecules, and their complementarity-determining regions (CDRs) form the primary antigen-recognition interface. Recent protein generative models have demonstrated broad capabilities in biomolecular design, yet post-training strategies for downstream objectives remain limited. Standard denoising training operates on noisy states obtained by perturbing native structures, whereas recursive generation proceeds through model-generated intermediate states. For flexible antibody CDR loops such as CDR-H3, this mismatch can allow backbone deviations to accumulate along the denoising trajectory and compromise antigen-facing loop geometry. We introduce ABOPD, an antibody design framework based on on-policy distillation that leverages privileged native geometry during training to supervise states visited along the model's own denoising trajectories. With this fine-grained structural supervision, ABOPD substantially improves structural recovery on RAbD CDR-H3 generation, reducing RMSD by 0.42 Å (from 2.37 Å to 1.95 Å) and outperforming supervised fine-tuning and offline distillation controls, offering a path to higher-fidelity protein design.

On-policy knowledge distillation transfers reasoning from large teachers to compact students, but existing approaches suffer three compounding failure modes: (i) cold-start collapse, where a fresh student assigns near-zero mass to teacher-preferred tokens; (ii) state-agnostic divergence scheduling, where time-only forward/reverse-KL interpolation ignores the student's coverage state; and (iii) binary reward sparsity, where pass/fail signals discard information from partially correct traces. We present CADENCE, a unified framework with a targeted fix for each. Its DRIFT mechanism schedules a per-token convex mixture of forward-KL and reverse-KL surrogate objectives on student-sampled trajectories (per-token surrogates, not sequence-level KL gradient estimators). Six components extend it: (A) COVA, a coverage-adaptive $β$ schedule accelerating the forward-to-reverse transition; (B) FTB, a forking-token boost concentrating gradient at high-entropy positions via a globally-normalized entropy reference; (C) CCD, a dense reward adding numerical-proximity partial credit for incorrect-but-close traces; (D) LAP, brevity-preferential correct-rollout reinforcement; (E) EMR, an entropy-matching calibration regularizer; (F) BSD, a bootstrapped self-distillation phase. On GSM8K and MATH-500 (corrected 512-token protocol, 5 seeds, reported std), CADENCE distills a 0.5B student from a 1.5B teacher to 69.8 $\pm$ 0.5% GSM8K pass@1 (from 48.7% pretrained; 63.2% of the teacher gap closed) and to 72.1 $\pm$ 0.4% with a 3B teacher (76.2% closed), beating the strongest matched-compute label-using baseline (DRIFT+binary reward) by +4.4 $\pm$ 0.7 points. All experiments run on a single Apple Mac Studio (M-series, 64GB unified memory), showing principled distillation reaches strong reasoning quality without datacenter-scale hardware.

Diffusion large language models (dLLMs) are a promising alternative to autoregressive generation. However, reasoning-oriented post-training for dLLMs remains challenging. Supervised fine-tuning (SFT) for dLLMs requires dense but often off-policy masked states, while reinforcement learning (RL) relies on sparse rewards or value modeling. This paper proposes \textbf{trace-based on-policy distillation (TOPD)}, a teacher-supervised framework that transfers reasoning ability to a target dLLM without reward estimation. The key idea is to supervise a dLLM on its own denoising trajectory, focusing on the trace-aligned token decisions that form the final response. Specifically, TOPD samples on-policy diffusion trajectories from the target dLLM, obtains teacher token distributions from a teacher model on the corresponding partially denoised states, and updates the target dLLM with a token-level Reverse Kullback-Leibler (Reverse-KL) objective. This design preserves dense teacher supervision while aligning training with the model's own denoising states. On mathematical reasoning benchmarks, TOPD enables SDAR-4B-Chat to match the MATH500 accuracy of its RL-trained counterpart TraDo-4B-Instruct, with gains of +5.7 under static evaluation and +4.5 under dynamic evaluation. Compared with the RL-trained counterpart, TOPD achieves this with 4$\times$ fewer rollout rounds, corresponding to an estimated 96.0$\times$ to-accuracy model-compute speedup.

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

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

Reinforcement learning with verifiable rewards (RLVR) commonly uses entropy for advantage shaping. However, entropy cannot distinguish useful uncertainty from detrimental confusion, limiting its effectiveness as a correctness signal. We propose Contrastive Policy Optimization (CPO), which uses token-level contrastive disagreement between reference-guided and vanilla generation distributions for correctness-aware advantage shaping. Both theoretical and empirical results show that this disagreement reliably indicates token-level correctness. We further show that On-policy Distillation is a special case of CPO, where the posterior distribution is instantiated by an external teacher model. CPO also resolves the zero-advantage problem. Experiments on in-domain and out-of-domain benchmarks demonstrate that CPO substantially outperforms entropy-based RLVR methods while maintaining strong generalization. Further analysis shows that correct and incorrect responses naturally support exploration and exploitation respectively, and balancing both leads to the best performance.

Large language models have made strong reasoning gains through supervised fine-tuning, reinforcement learning, and on-policy distillation, yet these post-training methods are usually evaluated only by final-answer accuracy. We study how they reshape confidence during reasoning. We introduce a three-stage calibration framework that evaluates confidence before, during, and after chain-of-thought generation, corresponding to difficulty estimation, early termination, and answer aggregation. Through a controlled comparison on mathematical reasoning benchmarks, we find that OPD provides the most useful pre-reasoning confidence, SFT gives the strongest online signal for early stopping, and RL produces the most reliable trace-level signal for aggregation. We further show that confidence reliability is position-dependent: RL confidence becomes informative after a path-commitment phase, while OPD confidence is useful early but can become inversely calibrated later. Based on this observation, we propose PosConf, a position-aware confidence strategy that uses confidence only from reliable relative-position intervals. PosConf improves RL answer aggregation by 6.1 points over majority voting and consistently improves OPD early stopping under tight token budgets, with gains up to 4.3 points by avoiding its later inverse-calibration region, showing that \emph{confidence in reasoning models should be used both stage-wise and position-awarely}. Our code is available at https://github.com/EIT-NLP/Post-Training-Calibration.

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

Structured pruning is a hardware-friendly way to compress LLMs, but it is mostly validated on multiple-choice recognition tasks, while the same compressed checkpoints can collapse on the free-form generation that deployment actually requires. Two observations trace this gap. First, greedy \textsc{pass}@$1$ nearly vanishes after compression, yet \textsc{pass}@$k$ recovers substantially under repeated sampling: useful generations are demoted, not erased. Second, the recoverable regime fails mainly through suffix repetition. Recovery should therefore train on the compressed model's own on-policy states with dense token-level supervision, which On-Policy Distillation (OPD) provides by reusing the pre-compression model as a frozen teacher. However, long on-policy rollouts spend early recovery budget on low-information repetitive suffixes, delaying loss descent. To mitigate this waste, we propose \textbf{\shortopd}, a short-to-long OPD schedule that detects teacher-confirmed repetitive suffixes, treats the surviving prefix as each rollout's effective length, and allocates future rollout budgets to the effective lengths the policy can currently use. Across math, code, and open-ended generation, \shortopd\ raises the compressed model's score to about $9\times$ its unrecovered value and $1.6$--$4.4\times$ standard recovery recipes (SFT w/o KD, KD, and SeqKD), and it matches a fixed $8192$-token rollout horizon within two points using a quarter of the training time ($8.5$ vs.\ $35.9$ hours) and $71\%$ fewer rollout tokens. We hope this recipe helps move structured pruning beyond marginal gains on perplexity and multiple-choice benchmarks, a step closer to deployment-ready generation quality.

Conventional language-model distillation often relies on fixed teacher-generated data, which may not cover the states encountered by an evolving student policy. On-policy distillation (OPD) instead collects teacher or evaluator supervision on student-generated rollouts. However, existing OPD methods differ substantially in supervision form, tokenizer compatibility, teacher access, and supervision granularity, leading to fragmented implementations that are difficult to reproduce and extend. We present \textsc{EasyOPD}, an on-policy distillation framework built on verl, a distributed reinforcement-learning framework for large language models. \textsc{EasyOPD} separates user-side configuration, method-specific supervision logic, and verl-based execution. Its method modules connect to the shared backend through extension boundaries for loss construction, rollout metadata, reward processing, tokenizer alignment, and teacher-side computation. We instantiate representative methods for three OPD settings -- cross-tokenizer OPD, on-policy self-distillation, and step-wise OPD. Experiments on reasoning, code-generation, scientific-knowledge, and tool-use benchmarks show that these implementations can be executed through the same verl-based backend while retaining their method-specific objectives and task-dependent performance profiles. We release \textsc{EasyOPD} with runnable YAML configurations, documentation, and an installable demonstration package and video.

We present Mach-Mind-4-Flash, a 35B-parameter Mixture-of-Experts (MoE) agentic model with 3B activated parameters. Through post-training optimization alone without scaling pre-training compute, the model achieves performance on par with or surpassing that of 100B-parameter-class models. By introducing scalable agentic interaction environments for large-scale reinforcement learning, the model attains significant performance gains on real-world application tasks. Our pipeline comprises three stages: (1) a unified RL/OPD training infrastructure with dynamic multi-teacher scheduling and operator-level acceleration, delivering 17% end-to-end training speedup; (2) multiple domain-specific RL experts trained in parallel across Reasoning, General, and Agent tracks, then fused into a single generalist via Multi-Teacher On-Policy Distillation (MOPD) -- a routed reverse-KL objective that eliminates the see-saw degradation of mixed-reward RL; (3) Hybrid Median-length Policy Optimization (HMPO), a single-stage token-efficiency method that compresses reasoning chains by 19--46% with $\le$0.7 percentage-point accuracy loss. Mach-Mind-4-Flash scores 92.70 on AIME'26, 82.82 on IFBench, 80.74 on Behavioral-SafetyBench, 75.80 on BFCL-v4, 72.31 on BrowseComp-zh, and 84.20 on ClawBench -- leading or matching models with 10--30$\times$ its activated size at a fraction of the inference cost.

Vision-Language Models (VLMs) have achieved success using homogeneous Transformers to process multimedia data. Recent studies show that heterogeneous structures interleaving efficient mechanisms, like linear attention, improve both performance and inference latency over homogeneous designs. However, these efforts rely on handcrafted static mixing patterns, which are sub-optimal and difficult to adapt to specific hardware. To bridge this gap, we propose Multi-Objective Search for Adaptive Inter-layer Composition (MOSAIC), a hardware-aware search method that automatically transforms homogeneous models into optimized heterogeneous architectures. MOSAIC integrates diverse efficiency mechanisms--including linear, sparse, and low-rank operators--into a unified search space. By formulating the selection as a multi-objective Mixed Integer Programming (MIP) problem, our method identifies optimal configurations that maximize downstream performance under strict hardware latency constraints. To mitigate performance degradation from structural transitions, we introduce a two-stage parameter recovery process: global off-policy distillation to stabilize internal representations, followed by a dual-teacher on-policy distillation leveraging a 235B oracle for knowledge expansion and the original 4B teacher for distributional stability. We validate MOSAIC through MOSAIC-4B, derived from Qwen3-VL-4B-Instruct. Results demonstrate that MOSAIC-4B matches the baseline's performance across multiple benchmarks while requiring less than 2% of the original training cost. Furthermore, it substantially improves inference efficiency, achieving 1.76x prefilling and 2.54x decoding speedups.

Agentic language models must learn when to call tools, when to consume tool responses, and when to answer directly. This makes multi-teacher on-policy distillation a natural training strategy: one teacher can specialize in tool calls, another in direct responses, and the student can learn from both on its own generated distribution. We show that this strategy can induce a behavior shift that is invisible from aggregate losses alone. In a two-teacher tool-use setting, vanilla generalized knowledge distillation improves tool-call recall but also moves the model toward over-calling, where it calls tools on examples that should be answered directly. Aggregate explanations are insufficient: tool-call samples do not receive more token exposure, and full-sequence per-token divergence is not larger for the tool-call teacher. We instead analyze behavior leverage imbalance: local token-level signals at mode- entry and structural positions, such as <tool_call> and function names, can have disproportionate control over the global generation mode. We propose Soft Clamp, a per-token divergence calibration method that dynamically compresses extreme token-level Jensen-Shannon divergence while preserving nonzero gradients. On APIGen-MT, Soft Clamp reduces over-calling from 13.7% to 9.0% relative to vanilla GKD while matching its decision accuracy. In a BFCL multi-turn diagnostic, it also lowers tool-call loops and repeated calls among GKD variants. These results suggest that multi-teacher OPD should monitor where teacher signals act, not only how large they are in aggregate.

On-policy distillation is a practical post-training recipe for large language models, supplying dense teacher supervision on the student's own trajectories. In privileged-context self-distillation, teacher and student are the same model conditioned on the same prefix, but the teacher also sees a hint or the full solution trace. This makes supervision abundant but harder to trust: the teacher can be confident about continuations its privileged view makes obvious but the student cannot yet justify. The distillation pull is strongest where teacher and student disagree most, and over many updates it accumulates into drift that degrades out-of-distribution (OOD) reasoning. We introduce GeoSD, a geometric self-distillation objective that treats this drift as movement in the student's predictive behavior and counters it in two complementary ways. A Hellinger loss scales each teacher preference by the overlap the student already shares with it, attenuating the pull on tokens the student cannot yet support. Since these pulls still compound over training, a proximal term penalizes how far the student's predictions drift from a recent checkpoint, measured as a Fisher-Rao distance. Both are distances in the same geometry of next-token distributions, and a natural-gradient update takes its steps in that geometry rather than in parameter space. Across mathematical reasoning benchmarks and three model families, GeoSD preserves the in-distribution gains of self-distillation while improving average OOD accuracy by 5.7-8.6 points over the base model, with gains holding across model scales from 1.7B to 32B. Analyzing why standard matching fails out of distribution, we find it wins agreement with the teacher by draining mass from alternatives at high-entropy states, resulting in confident agreement on wrong answers, whereas GeoSD keeps those alternatives in reach.

On-policy distillation (OPD) trains a student policy by matching a stronger teacher on the student's own trajectories, offering a promising framework for language agent training. However, its application to long-horizon agentic tasks remains insufficiently explored. We identify two key inefficiencies in vanilla agent OPD: (1) full-horizon rollouts often waste wall-clock resources on tail turns that provide weak and noisy KL supervision, and (2) trajectory-level KL objectives concentrate most of the loss on shallow tokens, leaving deeper decision turns under-trained once initial behaviors are aligned. To address these challenges, we propose TurnOPD, a turn-level budgeting strategy for efficient on-policy distillation of long-horizon agents. TurnOPD consists of two budget controllers: adaptive rollout-depth budgeting, which uses probe-based turn statistics to determine rollout length, and progressive turn-normalized loss budgeting, which gradually shifts KL weighting from token-level to turn-balanced supervision. Experiments on ALFWorld, WebShop, and Multi-Hop Search with task-specialized teacher models show that TurnOPD achieves superior validation accuracy under equal wall-clock training budgets and advances the accuracy--time frontier beyond vanilla OPD.

Reinforcement learning with verifiable rewards (RLVR) is a powerful recipe for improving language-model reasoning, but it is expensive to repeat on every new strong model because the target model must generate many rollouts during training. As models scale, post-training itself becomes a bottleneck. We study a weak-to-strong alternative: run RL on a smaller model where rollouts are cheaper, then reuse what that RL run learned to improve a stronger target model. Directly distilling the post-RL weak teacher is not enough, because the teacher's final policy mixes useful RL gains with the limitations of the smaller model. We propose Direct On-Policy Distillation (Direct-OPD), which transfers the teacher's RL-induced policy shift instead. Direct-OPD compares the post-RL teacher with its own pre-RL reference and treats their log-ratio as a dense implicit reward for the student. In plain terms, the checkpoint pair tells us which actions RL made the weak model more or less likely to take, and Direct-OPD applies that signal on the stronger student's own on-policy states. This directly reuses the weak model's RL supervision signal without running sparse-reward RL on the target model. Empirically, Direct-OPD consistently leverages weaker teachers to improve stronger target models; notably, it boosts Qwen3-1.7B from 48.3% to 58.3% on AIME 2024 in just 4 hours on 8 A100 GPUs. It outperforms step-matched direct RL and enables the sequential composition of multiple policy shifts. Our results show that RL outcomes can be reused across model scales as implicit reward signals, not merely as final models to imitate.

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

Big goals are hard to achieve all at once; breaking them into small steps is wiser. We present Trust Region Policy Distillation (TOP-D), which transforms the notoriously unstable, high-variance On-Policy Distillation (OPD) into a stable training paradigm by dynamically constructing a proximal teacher. Theoretically, we establish a rigorous framework demonstrating that TOP-D inherently controls gradient variance. By providing a formal global convergence analysis alongside a monotonic improvement bound, we mathematically formalize the reliability and stability of the overall training dynamics. Empirically, TOP-D dramatically enhances training stability, sample efficiency, and final performance on mathematical reasoning tasks. More importantly, TOP-D introduces zero additional computational overhead, positioning itself as a promising alternative to the well-established OPD paradigm.

Recent advances in multimodal foundation models and agent systems have driven GUI agents from single-platform task execution toward cross-platform interaction. However, building multi-platform GUI agents remains challenging. On one hand, high-quality and executable cross-platform interaction trajectories are still scarce, and existing data often suffer from limited platform coverage. On the other hand, different platforms exhibit distinct interaction conventions, making joint or continual training prone to behavioral pattern mixing, platform-specific capability degradation, and catastrophic forgetting. To address these challenges, we construct Uni-GUI, a high-quality cross-platform GUI interaction dataset, and propose UI-MOPD, the first method that incorporates multi-teacher on-policy distillation into continual learning for GUI agents. UI-MOPD dynamically selects a platform-specific teacher according to the current environment and transfers platform-specific behavioral priors to a shared policy through platform-conditioned distillation, enabling adaptation to new platforms while preserving capabilities on existing ones. Experiments on OSWorld and MobileWorld show that UI-MOPD achieves task success rates of 38.2% and 12.0%, respectively, demonstrating its effectiveness in balancing cross-platform capability retention and new-platform adaptation. Project page: https://elispectre.github.io/UI-MOPD/.

On-policy distillation is a powerful way to transfer reasoning ability from a strong teacher to a smaller student: the student samples trajectories from its own policy, and the teacher provides dense token-level supervision on the states the student actually visits. However, this supervision is not always reliable: a teacher can assign high likelihood to plausible but incorrect solutions, or low likelihood to correct student solutions that follow different reasoning paths. Unconditionally distilling the teacher can therefore reinforce bad modes or erase useful student behavior. To address these limitations, we introduce RG-OPD: Reward-Gated On-Policy Distillation that uses verifier feedback to decide when teacher logits should be trusted. RG-OPD bridges sparse verifier rewards and dense teacher logits, preserving token-level supervision while filtering misleading teacher signals. Across reasoning and coding benchmarks, RG-OPD produces stronger distilled students, outperforming both vanilla reverse-KL distillation and the recent TSD-KD baseline. At 1K generation length, RG-OPD improves over reverse-KL by 2.9 points and over TSD-KD by 4.9 points; in the long-generation setting, it improves over the untuned student by 8.2 points. Our code is available at https://github.com/UoC-tail/RG-OPD.

Generative reasoning re-rankers achieve strong recommendation accuracy by emitting a chain-of-thought before re-ordering a candidate list, but they are slow at inference: an autoregressive (AR) decoder spends one sequential forward pass per reasoning token, and the reasoning trace far exceeds the ranking it produces. To reduce this cost, block-diffusion language models decode many positions in parallel over a few denoising steps and are substantially faster, yet naively converting an AR re-ranker into one opens two accuracy gaps: (1) a structural gap: answer positions are denoised in parallel and scored independently, so the decoder emits invalid rankings (duplicated, dropped, or out-of-set identifiers) that AR avoids through left-to-right masking; and (2) a distributional gap: fine-tuning the converted model on fixed teacher trajectories is off-policy relative to its own decoding at inference, leaving a residual accuracy gap. To close both gaps while keeping the speedup, we propose \textbf{Diffusion-GR2}, a recipe that converts our AR reasoning re-ranker (GR2) into a block-diffusion re-ranker. First, conversion fine-tuning (CFT) adapts the AR-initialized diffusion model to denoise the answer into a valid permutation on its own, without an external constrained decoder. Next, on-policy distillation (OPD) then supervises the model on its own decoded trajectories with dense per-token targets from the AR teacher. Finally, we apply a reinforcement-learning (RL) stage against a re-ranking reward on top of OPD's on-policy policy. Experiments on Amazon Beauty demonstrate that Diffusion-GR2 recovers to near-parity with the AR re-ranker, while block-parallel decoding raises decode throughput by $2.4$--$3.5\times$ at the model's reasoning output length. Ablations show that CFT recovers most of the conversion gap, and that on-policy distillation further closes it to the AR reference.

On-policy distillation (OPD) has recently emerged as an effective post-training paradigm by providing supervision on student-generated trajectories. However, existing OPD methods for multimodal reasoning usually rely on a static teacher routing, assigning each sample to a single teacher based on modality or task type. This ignores that visual grounding and abstract reasoning may dominate different decoding steps, making a single teacher insufficient for the full trajectory. To this end, H-OPD is proposed as a confidence-aware heterogeneous multi-teacher OPD framework for multimodal reasoning. By verifying the complementarity of heterogeneous teachers in the same reasoning process, H-OPD replaces task or sample level teacher routing with token-level teacher arbitration along the shared student trajectory. H-OPD employs vision-to-language description transfer to enable text-only teachers to access key visual semantics, and uses a confidence-aware arbitration mechanism to dynamically combine vision-language teacher and text-only teachers at each token. Extensive evaluations over 11 widely-used reasoning benchmarks showcase the superior performance of our method.

Industrial recommendation systems serve billions of users through a multi-stage funnel -- retrieval, early-stage ranking, and re-ranking -- where the final re-ranking step disproportionately shapes user engagement and downstream performance, particularly for carousel and grid display formats. Despite growing enthusiasm for Large Language Models (LLMs) in recommendation, three gaps hinder industrial adoption: (1) most efforts target retrieval and ranking, leaving re-ranking -- the stage closest to the final user experience -- largely underexplored; (2) LLMs are typically deployed zero-shot or via supervised fine-tuning, underutilizing the reasoning capabilities unlocked by reinforcement learning (RL) on verifiable rewards; (3) deployed catalogs index billions of items with non-semantic identifiers that lie outside any base-LLM vocabulary. We present GR2 (Generative Reasoning Re-Ranker), an end-to-end framework that combines (i) mid-training on semantic IDs produced by a tokenizer with >=99% uniqueness, (ii) reasoning-trace distilled from a stronger teacher via targeted prompting and rejection sampling, and (iii) RL with verifiable rewards purpose-built for re-ranking. To make GR2 resource-viable, we further (iv) introduce a context compressor that amortizes training cost, On-Policy Distillation (OPD) as a scalable alternative to SFT -- which we find collapses at industrial scale -- and reasoning distillation for low-latency serving. GR2 delivers +18.7% R@1, +7.1% R@3, and +9.6% N@3 over legacy baselines on industrial-scale traffic. We further find that reward design is critical in re-ranking: LLMs often hack rewards by preserving the incoming order or exploiting position bias, motivating conditional verifiable rewards as essential industrial components.

Imitation Learning is a natural framework for learning in sequential decision-making systems and has emerged as the dominant paradigm through which we understand language model training. A central puzzle is that, while in theory offline IL can be horizon-free and optimal, in practice online methods such as on-policy distillation often outperform offline methods such as supervised fine-tuning. We propose a noisy expert model to explain this gap, in which the learner only has access to a noisy version of the expert's policy, but wishes to compete against the reward achieved by a clean expert, motivated by the fact that in many applications, e.g. training language models to perform long chains of thought, the expert is often imperfect. In this setting, we show a sharp separation between offline and online IL. Offline learning from noisy trajectories is fundamentally hard: to compete with the clean expert, the sample complexity must grow exponentially, in contradistinction to the clean expert setting where no explicit horizon dependence exists. In contrast, we prove that online interaction with the noisy expert via a novel variant of OPD enables polynomial dependence on the horizon in general. We further show that, under a natural condition on the expert noise distribution, which we show to be necessary for any horizon-free sample complexity, one can obtain such a guarantee, although our proposed algorithm sacrifices statistical efficiency in its dependence on the size of the policy class. Our analysis leads to an alternative loss function that is commonly considered empirically for LM training. We further provide algorithms and lower bounds, and extend our results to the more realistic setting of unknown corruption when the clean expert is deterministic, thereby providing a theoretical foundation for why OPD can outperform SFT when training language models from imperfect teachers.

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

Online imitation learning (IL), particularly on-policy distillation, has emerged as a strong LLM post-training approach, often outperforming offline supervised fine-tuning (SFT). Yet a principled understanding of when and why online interaction helps remains unclear. In this work, we challenge the view that error accumulation is the main source of online IL's advantage, and instead show that the benefits of online interaction depend critically on whether the setting is realizable, i.e., whether the student policy class can represent the expert policy. Under realizability, we empirically find that offline IL already matches expert performance. In contrast, in non-realizable (misspecified) settings, we prove that offline IL encounters an information-theoretic bottleneck even when horizon $H=1$, and propose a structural characterization of misspecification relative to the reward, under which online IL provably achieves high performance despite a large distributional mismatch between the expert and student policies.

Modern large language models (LLMs) rely on reinforcement learning during post-training to push specific capabilities, yet integrating multiple capabilities into one model remains hard. Existing methods, such as Off-Policy Finetune and Mix-RL, are either inefficient or lose performance. In this work, we propose Multi-teacher On-Policy Distillation (MOPD), a post-training paradigm for combining the capabilities of multiple domain RL teachers: we first run per-domain specialised RL to obtain a set of domain teachers, then distill these teachers into the student on its own rollouts. This eliminates exposure bias and provides a dense optimization signal. On Qwen3-30B-A3B, MOPD outperforms Mix-RL, Cascade RL, Off-Policy Finetune, and Param-Merge baselines, inheriting nearly all of each teacher's capability. MOPD also enables parallel, independent development of domain teachers, removing the cross-domain coupling typical of multi-domain post-training. MOPD has been deployed in the post-training of MiMo-V2-Flash, an industrial-scale frontier model, demonstrating its practical value for capability integration in frontier-scale LLMs.

A key step toward artificial general intelligence is to train models that can perform multiple tasks. In this paper, we study how to build such models by first training separate RL experts for individual tasks and then consolidating them via distillation, as an alternative to directly training a single model on mixed tasks. We show that off-policy distillation degrades in multi-task settings due to the mode-covering nature of forward KL: aggregating data from multiple tasks introduces a large number of behavioral modes that can exceed the student's capacity, forcing it to average across behaviors and leading to degraded performance. In contrast, on-policy distillation is mode-seeking but requires strong initialization. Inspired by these observations, we propose a two-phase approach: off-policy distillation followed by on-policy refinement. Evaluation across conversational agents and text-based games confirms that this two-phase approach matches single-task RL expert performance for each individual task, whereas off-policy or on-policy distillation alone fails to match this performance.

Group Relative Policy Optimization (GRPO) is a default recipe for process-supervised reinforcement learning of LLM reasoners, and dense process supervision -- via learned process reward models (PRMs) or on-policy-distillation KL signals -- is a common way to densify its otherwise weak outcome reward. Layering such a step-level signal on top of GRPO's group-standardized advantage, however, exposes three structural pathologies: \emph{channel contamination} between the pooled process, outcome, and format streams at group standardization; \emph{resolution mismatch} between the granularity of the process signal and the granularity of the logical decisions being credited; and a \emph{cumulative trap} by which GRPO's return-to-go sum surfaces either length inflation or truncated exploration depending on the sign regime of the signal. We propose \textbf{PASS} (\emph{Process Advantage Signal Shaping}), a compact middleware that sits between any scalar step-level process signal and GRPO's clipped surrogate and addresses the three pathologies in turn: \emph{Advantage Fusion} standardizes the three streams independently within each group, \emph{Chunk-by-Value} derives value-homogeneous chunks from the signal itself and broadcasts credit within each chunk, and \emph{Divide-Length} converts the cumulative objective into an average-value-density score. We validate PASS across two domains and two process-signal paradigms -- a learned PRM on mathematical reasoning and an on-policy-distillation KL signal (with a generalized variant) on multi-hop question answering -- and under two group-standardization operators. In every regime PASS delivers a consistent pass@1 gain over the corresponding GRPO baseline.

On-policy distillation (OPD) has a property absent in offline distillation and RL: teacher supervision quality depends on student competence. Incoherent rollouts yield noisy gradients; already-mastered tokens yield redundant ones. This creates waste at three scales (tokens, training phases, and prompts) yet existing methods supervise uniformly. We introduce SEAD, which uses entropy as a unified probe of this competence-dependent degradation at three scales: (1) joint teacher-student entropy partitions tokens into zones receiving tailored divergences or zero gradient (approx. 50% skipped); (2) a cosine schedule anneals from forward to reverse KL as competence grows; (3) a competence-gated curriculum introduces prompts easy-to-hard. These components are symbiotically necessary: token selection requires coherent rollouts (curriculum), annealing requires monotonic improvement (also curriculum). On OLMo-3 (7B to 32B), SEAD achieves +4.8 avg accuracy over vanilla OPD across six math benchmarks, with ablations confirming super-additive interactions.

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

We present Qwen-Image-2.0-RL, a post-training pipeline that applies reinforcement learning from human feedback (RLHF) and on-policy distillation (OPD) to improve both the visual quality and instruction-following capability of the Qwen-Image-2.0 diffusion model. To provide reliable reward signals, we construct task-specific composite reward models by fine-tuning vision-language models with a pointwise scoring paradigm and chain-of-thought reasoning. For text-to-image generation, the reward models cover alignment, aesthetics, and portrait fidelity dimensions. For image editing tasks, the reward system addresses instruction-following accuracy and face identity preservation. Building on this reward system, we develop a scalable GRPO-based RL training framework, incorporating a hybrid classifier-free guidance (CFG) strategy to preserve pre-trained knowledge, prompt curation via intra-group reward range filtering, and per-category reward weight calibration. To merge the task-specialized RL policies for T2I and editing, we propose on-policy distillation as the final training stage, which consolidates multiple teachers into a single student model through trajectory-level velocity matching. Extensive evaluation shows that Qwen-Image-2.0-RL achieves 57.84 overall score on Qwen-Image-Bench (+2.61 over the base model), Elo ratings of 1193 in text-to-image arena (+78) and 1349 in image edit arena (+93), demonstrating consistent gains in aesthetic quality, prompt adherence, and editing accuracy.

Modern image generation demands a single model that unifies diverse capabilities, including text-to-image (T2I), local editing, and global editing. However, these capabilities are rarely naturally aligned and often conflict. For instance, editing tends to degrade T2I performance, while global and local editing interfere with each other. Consequently, effectively composing these capabilities has become a central challenge for image generation model training. To tackle this, we introduce DanceOPD, an on-policy generative field distillation framework for flow-matching models that routes each sample to one capability field, queries one low-noise student-induced state, and trains with a simple velocity MSE objective. With each capability source defined as a velocity field over the shared flow state space, the student learns from fields queried on its own rollout states to compose expert capabilities. This formulation also absorbs operator-defined fields such as classifier-free guidance. Comprehensive experiments on T2I, editing, realism-field absorption, and CFG absorption show that our approach improves multi-capability composition, strengthening target capabilities while preserving anchor generation quality. We believe this work establishes a practical route for generative field distillation in flow-matching models.

Fine-grained visual reasoning requires multimodal large language models (MLLMs) to identify task-relevant visual evidence and ground their reasoning in local image regions. Existing agentic methods typically rely on reinforcement learning with verifiable rewards or supervised fine-tuning on large-scale annotated reasoning traces, leading to costly exploration, hand-designed verification rules, or heavy dependence on textual supervision. A natural way to avoid such external answer labels is to learn from trajectories sampled by the student itself, which points to On-Policy Distillation (OPD). To understand what OPD can and cannot provide for visual reasoning, we revisit it as negative-free stop-gradient alignment. This perspective shows that, although OPD provides effective token-level correction, its ceiling is constrained by the absence of trajectory-level discrimination. Motivated by these observations, we propose V-Zero, an answer-label-free framework for visual reasoning with contrastive evidence gating. V-Zero uses no annotated textual answer labels; instead, during training it pairs a question-relevant regional crop with a negative visual view to evaluate student-sampled trajectories and gate dense token-level distillation. Experiments on multiple visual reasoning benchmarks show that V-Zero consistently improves fine-grained visual reasoning while preserving strong generalization. Notably, V-Zero is more than 5$\times$ faster than previous supervised fine-tuning methods and more than 10$\times$ faster than reinforcement learning baselines. Code and dataset will be released at https://github.com/eVI-group-SCU/V-Zero

On-policy distillation (OPD) trains a student on its own rollouts guided by teacher feedback and is becoming increasingly important for large language model (LLM) post-training. Like reinforcement learning (RL), however, OPD faces an on-policy systems bottleneck, as rollouts can dominate training time for reasoning workloads. Asynchronous training pipelines can alleviate this bottleneck by decoupling rollout generation from learner updates, but doing so introduces stale-policy data. While prior work has studied stale data in asynchronous RL, its effects in OPD remain underexplored. We present the first systematic study of staleness in asynchronous OPD, focusing on a practical setting where teacher feedback is implemented through local KL losses and full-vocabulary teacher logits are too expensive to store or transfer, necessitating finite teacher-score caches. We first show that KL direction changes the stale-data problem: teacher-weighted forward KL is more robust to stale rollouts, whereas student-weighted reverse KL is vulnerable. Second, for this vulnerable reverse-KL case, we study whether methods designed to stabilize asynchronous RL can mitigate OPD staleness. In our experiments, they do not improve over a simpler OPD-specific surrogate: recomputing the reverse-KL signal under the current student at learner time. Third, we analyze how finite teacher-score caches create a bias-variance tradeoff for sparse and sampled reverse-KL OPD estimators. This motivates multi-sample Monte Carlo (MC), which preserves MC correctability while reducing one-sample variance. Finally, we present and open-source AsyncOPD, a fully asynchronous OPD training pipeline built from these estimator choices. Experiments show that AsyncOPD improves training throughput by $1.6\times$ to $3.8\times$ over strict synchronous training while reaching comparable accuracy.

On-policy distillation (OPD) trains a student policy using teacher signals computed on trajectories sampled by the student itself. Recent work shows that sampled-token OPD can be fragile on long-horizon reasoning tasks and that local teacher-support matching is a simple and effective repair. This paper introduces blockwise policy-drift gating, a lightweight student-only old-current drift controller for OPD under rollout reuse. The method computes log-probability shifts between the behavior student and the current student on the sampled token path, aggregates these shifts over fixed blocks or spans, and uses the resulting detached, mean-normalized gates to reweight OPD position losses. It does not change teacher targets, teacher top-K supports, or the rollout policy. In a six-variant Qwen3 math reasoning benchmark with a uniform 200-step training budget for all trained variants, we use pass@8 as the primary problem-level solve-rate metric. Fixed 64-token block gating improves sampled-token OPD mean pass@8 from 0.4978 to 0.5160 across AIME24, AIME25, MATH500, and AMC23. On Teacher-TopK/LSM, Block64 gives the best four-benchmark mean pass@8 among trained students. The results identify local old-current policy drift as a practical control signal for reused OPD rollouts and motivate block-level gating as a simple default for improving solve-rate robustness.

On-policy distillation (OPD) improves LLM reasoning by training a student model on its own generated outputs, but standard OPD treats all student-generated outputs (SGOs) equally regardless of their informativeness. We observe a consistent asymmetry in controlled filtering experiments: in both OPD and on-policy self distillation (OPSD), training only on incorrect SGOs outperforms training only on correct ones. Our further analysis suggests that models trained on correct-only SGOs tend to generate shorter reasoning traces and show weaker reflection behavior, while incorrect SGOs better preserve exploratory reasoning near the model's capability boundary. To exploit this signal without requiring full answer-containing rollouts, we introduce ReNIO, which Reweights Negative trajectory Importance for LLM On-policy distillation. By using the student-to-teacher probability ratio, ReNIO identifies pivotal tokens leading to wrong reasoning traces and aggregates their information into a normalized sample weight, inherently assigning larger weights to likely negative trajectories without observing the correctness of final-answer. Since Re-NIO only uses prefix-conditioned token probabilities, it preserves OPD's prefix training advantage over full-rollout reinforcement learning. Across both mathematical reasoning and code generation tasks, ReNIO improves both OPD and OPSD, with representative relative gains of up to 8.90% for Qwen3-1.7B and 10.00% for R1-Distill-Qwen-7B on mathematical reasoning benchmarks. Code repo: https://github.com/BDML-lab/ReNIO.

On-policy distillation transfers reasoning ability through dense token-level supervision, yet the nature of the transferable signal remains unclear. We discover that reasoning chains contain two types of knowledge that require different discovery mechanisms: decisions (where to branch), which surface through student uncertainty, and evidence (intermediate steps that justify decisions), which hides in positions where the student is confident yet wrong. Current methods capture only decisions; the substantive knowledge in evidence tokens remains untransferred. We propose DEAR(Decision-Evidence Aware Reasoning Distillation), which first identifies decisions via student entropy, then discovers their supporting evidence through hidden-state cosine similarity to decision anchors, boosted by teacher-student divergence to prioritize the largest knowledge gaps. Across three student-teacher configurations on math and code benchmarks, DEAR consistently outperforms standard OPD, with up to +2.5pp on competition math and +5.7pp on code generation.