AR-OPD disentangles privileged supervision via anchored residual guidance to reduce hindsight leakage in on-policy distillation, reporting gains of 2.3 points over full privileged OPD and 7.9 over SFT on reasoning tasks.
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Privileged Information Distillation for Language Models
Canonical reference. 75% of citing Pith papers cite this work as background.
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abstract
Training-time privileged information (PI) can enable language models to succeed on tasks they would otherwise fail, making it a powerful tool for reinforcement learning in hard, long-horizon settings. However, transferring capabilities learned with PI to policies that must act without it at inference time remains a fundamental challenge. We study this problem in the context of distilling frontier models for multi-turn agentic environments, which typically hide their internal reasoning and expose only action trajectories. This breaks standard distillation pipelines, since successful behavior is observable, but the reasoning process is not. For this, we introduce {\pi}-Distill, a joint teacher-student objective that trains a PI-conditioned teacher and an unconditioned student simultaneously using the same model. Additionally, we also introduce On-Policy Self-Distillation (OPSD), an alternative approach that trains using Reinforcement Learning (RL) with a reverse KL-penalty between the student and the PI-conditioned teacher. We show that both of these algorithms effectively distill frontier agents using action-only PI. Specifically, we find that {\pi}-Distill and, in some cases, OPSD, outperform industry standard practices (Supervised finetuning followed by RL) that assume access to full Chain-of-Thought supervision across multiple agentic benchmarks, models, and forms of PI. We complement our results with extensive analysis that characterizes the factors enabling effective learning with PI, focusing primarily on {\pi}-Distill and characterizing when OPSD is competitive.
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2026 35representative citing papers
Self-Policy Distillation extracts a capability subspace from model gradients on correctness tokens, projects KV activations into it for self-generation, and fine-tunes LLMs to achieve up to 13-16% gains over baselines without external signals.
CEPO sharpens token credit in RLVR by requiring tokens to be favored by the correct answer and disfavored by wrong answers drawn from rejected rollouts, delivering accuracy gains on five multimodal math benchmarks.
Next-acceleration-scale autoregressive prediction in discrete latent space with on-policy privileged information distillation yields improved MRI reconstructions from sparse measurements on the fastMRI benchmark.
VPD frames language feedback learning as variational EM so the teacher policy refines itself via trust-region updates on outcomes while the student learns dense token distributions on its own rollouts, outperforming fixed-teacher baselines on reasoning and code tasks.
Self-distillation token rewards measure input-response-feedback pointwise mutual information, and CREDIT extracts the input-specific component with contrastive baselines to improve LLM reasoning performance.
Distillation signals align better with ideal updates on incorrect student rollouts than correct ones, with optimal teacher context depending on student capacity and task.
TRACE improves math reasoning by distilling only on annotator-marked critical spans with forward KL on correct key spans, optional reverse KL on errors, and GRPO elsewhere, gaining 2.76 points over GRPO while preserving OOD performance.
MAD-OPD recasts on-policy distillation teachers as a debating collective to supply better supervision, lifting agentic and code performance over single-teacher OPD across multiple model sizes.
TCOD stabilizes on-policy distillation for multi-turn agents via temporal curriculum on trajectory depth, improving performance up to 18 points over vanilla OPD and sometimes surpassing the teacher.
Self-play’s natural question-construction paths supply free privileged information that turns sparse-reward self-play into dense self-distillation, yielding stronger data-free search agents.
A geometric self-distillation objective using Hellinger loss and Fisher-Rao proximal regularization prevents predictive drift in LLM post-training, improving out-of-distribution reasoning by 5.7-8.6 points.
RAPS-DA improves RAG robustness to heterogeneous knowledge conflicts by training regime-specific peer specialists with hard routing and a dual-layer token selector for focused supervision.
On-policy self-distillation with sampled demonstrations reduces rollout diversity by amplifying existing probability gaps in the base model, unlike ideal RL which preserves ratios among correct outputs.
ROAD-VLA constructs an advantage-perturbed proximal teacher in action space to convert sparse rewards into dense supervision for online VLA adaptation and reports outperformance versus PPO across seven manipulation environments.
Visual-SDPO distills visual feedback from rendered code outputs into a student policy via grounded credit weighting and GRPO, yielding over 10-point gains on chart/UI/slide benchmarks.
A teacher-student reward model learns reasoning-conditioned score distributions for text-to-image images, yielding ~89% preference accuracy and a 41% net human-preference gain when used for generator optimization.
DASD improves math reasoning in LLMs by adaptively directing self-distillation based on per-token entropy to balance exploration and step accuracy, outperforming prior self-distillation and RLVR baselines on six benchmarks.
Experiments on coding and deterministic tasks demonstrate that data gating is sufficient for self-play stability while reward variants are not, revealing the Grounded Proposer Paradox and a two-stage phase transition under continuous gate strictness.
RESD turns failure trajectories into token-level supervision via retrospective reflections and a persistent global playbook, enabling faster improvement than standard self-distillation or GRPO with only one rollout per prompt.
MOPD improves on-policy distillation by using peer successes and failures from multiple rollouts to construct more informative teacher signals, yielding consistent gains over baselines on reasoning benchmarks.
UniSD unifies self-distillation components for autoregressive LLMs and its full integrated version improves base models by 5.4 points and baselines by 2.8 points across six benchmarks.
D-OPSD formulates supervised fine-tuning of step-distilled diffusion models as on-policy self-distillation by having the model act as both teacher (with multimodal context) and student (with text-only context) on its own roll-outs.
Reward-weighted classifier-free guidance approximates Q-function policy improvement in autoregressive models, enabling test-time reward optimization and faster RL convergence via distillation.
citing papers explorer
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Beyond Absolute Imitation: Anchored Residual Guidance for Privileged On-Policy Distillation
AR-OPD disentangles privileged supervision via anchored residual guidance to reduce hindsight leakage in on-policy distillation, reporting gains of 2.3 points over full privileged OPD and 7.9 over SFT on reasoning tasks.
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Self-Policy Distillation via Capability-Selective Subspace Projection
Self-Policy Distillation extracts a capability subspace from model gradients on correctness tokens, projects KV activations into it for self-generation, and fine-tunes LLMs to achieve up to 13-16% gains over baselines without external signals.
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CEPO: RLVR Self-Distillation using Contrastive Evidence Policy Optimization
CEPO sharpens token credit in RLVR by requiring tokens to be favored by the correct answer and disfavored by wrong answers drawn from rejected rollouts, delivering accuracy gains on five multimodal math benchmarks.
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Next-Acceleration-Scale Prediction for Autoregressive MRI Reconstruction
Next-acceleration-scale autoregressive prediction in discrete latent space with on-policy privileged information distillation yields improved MRI reconstructions from sparse measurements on the fastMRI benchmark.
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Learning from Language Feedback via Variational Policy Distillation
VPD frames language feedback learning as variational EM so the teacher policy refines itself via trust-region updates on outcomes while the student learns dense token distributions on its own rollouts, outperforming fixed-teacher baselines on reasoning and code tasks.
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From Generic Correlation to Input-Specific Credit in On-Policy Self Distillation
Self-distillation token rewards measure input-response-feedback pointwise mutual information, and CREDIT extracts the input-specific component with contrastive baselines to improve LLM reasoning performance.
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Unmasking On-Policy Distillation: Where It Helps, Where It Hurts, and Why
Distillation signals align better with ideal updates on incorrect student rollouts than correct ones, with optimal teacher context depending on student capacity and task.
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TRACE: Distilling Where It Matters via Token-Routed Self On-Policy Alignment
TRACE improves math reasoning by distilling only on annotator-marked critical spans with forward KL on correct key spans, optional reverse KL on errors, and GRPO elsewhere, gaining 2.76 points over GRPO while preserving OOD performance.
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MAD-OPD: Breaking the Ceiling in On-Policy Distillation via Multi-Agent Debate
MAD-OPD recasts on-policy distillation teachers as a debating collective to supply better supervision, lifting agentic and code performance over single-teacher OPD across multiple model sizes.
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TCOD: Exploring Temporal Curriculum in On-Policy Distillation for Multi-turn Autonomous Agents
TCOD stabilizes on-policy distillation for multi-turn agents via temporal curriculum on trajectory depth, improving performance up to 18 points over vanilla OPD and sometimes surpassing the teacher.
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$\pi$-Play: Multi-Agent Self-Play via Privileged Self-Distillation without External Data
Self-play’s natural question-construction paths supply free privileged information that turns sparse-reward self-play into dense self-distillation, yielding stronger data-free search agents.
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Geometric Self-Distillation for Reasoning Generalization
A geometric self-distillation objective using Hellinger loss and Fisher-Rao proximal regularization prevents predictive drift in LLM post-training, improving out-of-distribution reasoning by 5.7-8.6 points.
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Regime-Aware Peer Specialization for Robust RAG under Heterogeneous Knowledge Conflicts
RAPS-DA improves RAG robustness to heterogeneous knowledge conflicts by training regime-specific peer specialists with hard routing and a dual-layer token selector for focused supervision.
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On-Policy Self-Distillation with Sampled Demonstrations Reduces Output Diversity
On-policy self-distillation with sampled demonstrations reduces rollout diversity by amplifying existing probability gaps in the base model, unlike ideal RL which preserves ratios among correct outputs.
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ROAD-VLA: Robust Online Adaptation via Self-Distillation for Vision-Language-Action Models
ROAD-VLA constructs an advantage-perturbed proximal teacher in action space to convert sparse rewards into dense supervision for online VLA adaptation and reports outperformance versus PPO across seven manipulation environments.
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Self-Distillation Policy Optimization via Visual Feedback: Bridging Code and Visual Artifacts
Visual-SDPO distills visual feedback from rendered code outputs into a student policy via grounded credit weighting and GRPO, yielding over 10-point gains on chart/UI/slide benchmarks.
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Z-Reward: Beyond Scalar Rewards by Internalizing Reasoning into Score Distributions
A teacher-student reward model learns reasoning-conditioned score distributions for text-to-image images, yielding ~89% preference accuracy and a 41% net human-preference gain when used for generator optimization.
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Tailoring Teaching to Aptitude: Direction-Adaptive Self-Distillation for LLM Reasoning
DASD improves math reasoning in LLMs by adaptively directing self-distillation based on per-token entropy to balance exploration and step accuracy, outperforming prior self-distillation and RLVR baselines on six benchmarks.
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Survive or Collapse: The Asymmetric Roles of Data Gating and Reward Grounding in Self-Play RL
Experiments on coding and deterministic tasks demonstrate that data gating is sufficient for self-play stability while reward variants are not, revealing the Grounded Proposer Paradox and a two-stage phase transition under continuous gate strictness.
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Learning with Rare Success but Rich Feedback via Reflection-Enhanced Self-Distillation
RESD turns failure trajectories into token-level supervision via retrospective reflections and a persistent global playbook, enabling faster improvement than standard self-distillation or GRPO with only one rollout per prompt.
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Multi-Rollout On-Policy Distillation via Peer Successes and Failures
MOPD improves on-policy distillation by using peer successes and failures from multiple rollouts to construct more informative teacher signals, yielding consistent gains over baselines on reasoning benchmarks.
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UniSD: Towards a Unified Self-Distillation Framework for Large Language Models
UniSD unifies self-distillation components for autoregressive LLMs and its full integrated version improves base models by 5.4 points and baselines by 2.8 points across six benchmarks.
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D-OPSD: On-Policy Self-Distillation for Continuously Tuning Step-Distilled Diffusion Models
D-OPSD formulates supervised fine-tuning of step-distilled diffusion models as on-policy self-distillation by having the model act as both teacher (with multimodal context) and student (with text-only context) on its own roll-outs.
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Reward Weighted Classifier-Free Guidance as Policy Improvement in Autoregressive Models
Reward-weighted classifier-free guidance approximates Q-function policy improvement in autoregressive models, enabling test-time reward optimization and faster RL convergence via distillation.
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Lightning OPD: Efficient Post-Training for Large Reasoning Models with Offline On-Policy Distillation
Lightning OPD is an offline on-policy distillation method that matches standard OPD performance at 4x efficiency by enforcing teacher consistency between SFT and distillation phases.
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Skill-SD: Skill-Conditioned Self-Distillation for Multi-turn LLM Agents
Skill-SD turns an agent's completed trajectories into dynamic natural-language skills that condition only the teacher in self-distillation, yielding 14-42% gains over RL and OPSD baselines on multi-turn agent benchmarks.
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Learning beyond Teacher: Generalized On-Policy Distillation with Reward Extrapolation
Generalized on-policy distillation with reward scaling above one (ExOPD) lets student models surpass teacher performance when merging domain experts on math and code tasks.
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TREK: Distill to Explore, Reinforce to Refine
TREK uses verified teacher proposals to expand a student model's exploration support before standard GRPO refinement, improving performance on hard math and agentic tasks.
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DOPD: Dual On-policy Distillation
DOPD is an advantage-aware dual distillation method that dynamically assigns token supervision from either privileged teacher or student to transfer capability while mitigating non-replicable information asymmetry in on-policy distillation.
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HERO: Hindsight-Enhanced Reflection from Environment Observations for Agentic Self-Distillation
HERO converts environment observations after each turn into compact diagnoses to provide aligned feedback for self-distillation, improving success rates and reducing unnecessary actions on TauBench and WebShop compared to baselines.
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StepOPSD: Step-Aware Online Preference Distillation for Agent Reinforcement Learning
StepOPSD introduces step-aware online preference distillation for agent RL, achieving top or near-top results on ALFWorld and Search-QA subsets by using per-step credit shaping.
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Signal Reshaping for GRPO in Weak-Feedback Agentic Code Repair
Reshaping outcome rewards, process signals, and rollout comparability in GRPO raises strict compile-and-semantic accuracy in agentic code repair from 0.385 to 0.535 under weak feedback.
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Self-Distilled Policy Gradient
SDPG combines group-relative verifier advantages, normalized standard deviation, full-vocabulary on-policy self-distillation, and reference-policy KL regularization to improve stability and performance over RLVR and self-distillation baselines in language model RL.
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A Brief Overview: On-Policy Self-Distillation In Large Language Models
This overview paper explains the conceptual foundations and design principles of On-Policy Self-Distillation for large language models from a beginner's perspective.
- SOD: Step-wise On-policy Distillation for Small Language Model Agents