# Self-Distilled RLVR

arXiv: https://arxiv.org/abs/2604.03128 · HTML: https://mlsanity.com/paper/2604.03128/

## Key facts

- Cited by 131 papers in the map (data through 14 Oct 2026).
- Placed in On-policy and self-distillation for LLMs, one of 12 directions in Knowledge distillation.
- Builds on 30 of its 35 references that are in the map.
- First posted on arXiv 3 Apr 2026.

## Placed in

- Knowledge distillation / [On-policy and self-distillation for LLMs](https://mlsanity.com/distill/on-policy-and-self-distillation-for-llms/)

## Builds on (most cited first, 30 of 30)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [MathVista: Evaluating Mathematical Reasoning of Foundation Models in Visual Contexts](https://mlsanity.com/paper/2310.02255/) (2023)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [Process Reinforcement through Implicit Rewards](https://mlsanity.com/paper/2502.01456/) (2025)
- [Generative Verifiers: Reward Modeling as Next-Token Prediction](https://mlsanity.com/paper/2408.15240/) (2024)
- [Self-Distilled Reasoner: On-Policy Self-Distillation for Large Language Models](https://mlsanity.com/paper/2601.18734/) (2026)
- [Improve Mathematical Reasoning in Language Models by Automated Process Supervision](https://mlsanity.com/paper/2406.06592/) (2024)
- [We-Math: Does Your Large Multimodal Model Achieve Human-like Mathematical Reasoning?](https://mlsanity.com/paper/2407.01284/) (2024)
- [Reasoning with Exploration: An Entropy Perspective](https://mlsanity.com/paper/2506.14758/) (2025)
- [Self-Distillation Enables Continual Learning](https://mlsanity.com/paper/2601.19897/) (2026)
- [Dynamic Early Exit in Reasoning Models](https://mlsanity.com/paper/2504.15895/) (2025)
- [On-Policy Context Distillation for Language Models](https://mlsanity.com/paper/2602.12275/) (2026)
- [Revisiting On-Policy Distillation: Empirical Failure Modes and Simple Fixes](https://mlsanity.com/paper/2603.25562/) (2026)
- [Privileged Information Distillation for Language Models](https://mlsanity.com/paper/2602.04942/) (2026)
- [SEED-GRPO: Semantic Entropy Enhanced GRPO for Uncertainty-Aware Policy Optimization](https://mlsanity.com/paper/2505.12346/) (2025)
- [S-GRPO: Early Exit via Reinforcement Learning in Reasoning Models](https://mlsanity.com/paper/2505.07686/) (2025)
- [Step-level Value Preference Optimization for Mathematical Reasoning](https://mlsanity.com/paper/2406.10858/) (2024)
- [ZeroBench: An Impossible Visual Benchmark for Contemporary Large Multimodal Models](https://mlsanity.com/paper/2502.09696/) (2025)
- [Unlocking Exploration in RLVR: Uncertainty-aware Advantage Shaping for Deeper Reasoning](https://mlsanity.com/paper/2510.10649/) (2025)
- [MMFineReason: Closing the Multimodal Reasoning Gap via Open Data-Centric Methods](https://mlsanity.com/paper/2601.21821/) (2026)
- [Attention Illuminates LLM Reasoning: The Preplan-and-Anchor Rhythm Enables Fine-Grained Policy Optimization](https://mlsanity.com/paper/2510.13554/) (2025)
- [KTAE: A Model-Free Algorithm to Key-Tokens Advantage Estimation in Mathematical Reasoning](https://mlsanity.com/paper/2505.16826/) (2025)
- [Outcome-Grounded Advantage Reshaping for Fine-Grained Credit Assignment in Mathematical Reasoning](https://mlsanity.com/paper/2601.07408/) (2026)
- [Test-time Prompt Intervention](https://mlsanity.com/paper/2508.02511/) (2025)
- [Beyond High-Entropy Exploration: Correctness-Aware Low-Entropy Segment-Based Advantage Shaping for Reasoning LLMs](https://mlsanity.com/paper/2512.00908/) (2025)

## Built on by (most cited first, 30 of 131)

- [Rethinking On-Policy Distillation of Large Language Models: Phenomenology, Mechanism, and Recipe](https://mlsanity.com/paper/2604.13016/) (2026)
- [Uni-OPD: Unifying On-Policy Distillation with a Dual-Perspective Recipe](https://mlsanity.com/paper/2605.03677/) (2026)
- [RLCSD: Reinforcement Learning with Contrastive On-Policy Self-Distillation](https://mlsanity.com/paper/2606.11709/) (2026)
- [Rethinking On-Policy Self-Distillation for Thinking Models](https://mlsanity.com/paper/2607.05184/) (2026)
- [Filter, Then Reweight: Rethinking Optimization Granularity in On-Policy Distillation](https://mlsanity.com/paper/2606.02684/) (2026)
- [OPID: On-Policy Skill Distillation for Agentic Reinforcement Learning](https://mlsanity.com/paper/2606.26790/) (2026)
- [Respecting Self-Uncertainty in On-Policy Self-Distillation for Efficient LLM Reasoning](https://mlsanity.com/paper/2605.13255/) (2026)
- [D-OPSD: On-Policy Self-Distillation for Continuously Tuning Step-Distilled Diffusion Models](https://mlsanity.com/paper/2605.05204/) (2026)
- [SOD: Step-wise On-policy Distillation for Small Language Model Agents](https://mlsanity.com/paper/2605.07725/) (2026)
- [Privileged, but Biased: How PI-Conditioned Teachers Break Self-Distillation](https://mlsanity.com/paper/2608.04794/) (2026)
- [MAD-OPD: Breaking the Ceiling in On-Policy Distillation via Multi-Agent Debate](https://mlsanity.com/paper/2605.01347/) (2026)
- [On-Policy Self-Distillation without Any Supervision](https://mlsanity.com/paper/2608.06296/) (2026)
- [STEPS: Selective On-Policy Self-Distillation for Reasoning](https://mlsanity.com/paper/2605.10194/) (2026)
- [OGLS-SD: On-Policy Self-Distillation with Outcome-Guided Logit Steering for LLM Reasoning](https://mlsanity.com/paper/2605.12400/) (2026)
- [Rebellious Student: Reversing Teacher Signals for Reasoning Exploration with Self-Distilled RLVR](https://mlsanity.com/paper/2605.10781/) (2026)
- [On-policy Distillation with Verifiable Reward](https://mlsanity.com/paper/2608.24696/) (2026)
- [Anti-Self-Distillation for Reasoning RL via Pointwise Mutual Information](https://mlsanity.com/paper/2605.11609/) (2026)
- [Preference-Based Self-Distillation: Beyond KL Matching via Reward Regularization](https://mlsanity.com/paper/2605.05040/) (2026)
- [GEAR: Granularity-Adaptive Advantage Reweighting for LLM Agents via Self-Distillation](https://mlsanity.com/paper/2605.11853/) (2026)
- [ViCuR: Visual Cues as Recoverable Privilege for Multimodal On-Policy Distillation](https://mlsanity.com/paper/2606.05718/) (2026)
- [UCOB: Learning to Utilize and Evolve Agentic Skills via Credit-Aware On-Policy Bidirectional Self-Distillation](https://mlsanity.com/paper/2606.29502/) (2026)
- [DOPD: Dual On-policy Distillation](https://mlsanity.com/paper/2606.30626/) (2026)
- [Learn where to Click from Yourself: On-Policy Self-Distillation for GUI Grounding](https://mlsanity.com/paper/2605.00642/) (2026)
- [Beyond GRPO and On-Policy Distillation: An Empirical Sparse-to-Dense Reward Principle for Language-Model Post-Training](https://mlsanity.com/paper/2605.12483/) (2026)
- [OPRD: On-Policy Representation Distillation](https://mlsanity.com/paper/2606.06021/) (2026)
- [V-Zero: Answer-Label-Free On-Policy Distillation with Contrastive Evidence Gating for Fine-Grained Visual Reasoning](https://mlsanity.com/paper/2606.25319/) (2026)
- [Does On-Policy Distillation Really Distill? From Noisy Teacher to Self-Improvement](https://mlsanity.com/paper/2608.31046/) (2026)
- [VISD: Enhancing Video Reasoning via Structured Self-Distillation](https://mlsanity.com/paper/2605.06094/) (2026)
- [Training with Harnesses: On-Policy Harness Self-Distillation for Complex Reasoning](https://mlsanity.com/paper/2605.08741/) (2026)
- [Tailoring Teaching to Aptitude: Direction-Adaptive Self-Distillation for LLM Reasoning](https://mlsanity.com/paper/2605.22263/) (2026)

## Abstract (arXiv)

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