# Train Ahead, Distill Back: Bootstrapping On-Policy Self-Distillation for Large Language Models

arXiv: https://arxiv.org/abs/2609.37132 · HTML: https://mlsanity.com/paper/2609.37132/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Self-rewarding alignment and self-training, one of 13 directions in Synthetic data and self-improvement for LLMs.
- Builds on 23 of its 40 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Placed in

- Synthetic data and self-improvement for LLMs / [Self-rewarding alignment and self-training](https://mlsanity.com/synth/self-rewarding-alignment-and-self-training/)
- 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, 23 of 23)

- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Self-Distilled RLVR](https://mlsanity.com/paper/2604.03128/) (2026)
- [Privileged Information Distillation for Language Models](https://mlsanity.com/paper/2602.04942/) (2026)
- [Unifying Group-Relative and Self-Distillation Policy Optimization via Sample Routing](https://mlsanity.com/paper/2604.02288/) (2026)
- [GATES: Self-Distillation under Privileged Context with Consensus Gating](https://mlsanity.com/paper/2602.20574/) (2026)
- [Purified OPSD: On-Policy Self-Distillation Without Losing How to Think](https://mlsanity.com/paper/2607.02234/) (2026)
- [On-Policy Self-Distillation without Any Supervision](https://mlsanity.com/paper/2608.06296/) (2026)
- [OGLS-SD: On-Policy Self-Distillation with Outcome-Guided Logit Steering for LLM Reasoning](https://mlsanity.com/paper/2605.12400/) (2026)
- [Rethinking Reward Supervision: Rubric-Conditioned Self-Distillation](https://mlsanity.com/paper/2606.19327/) (2026)
- [Reducing the Safety Tax in LLM Safety Alignment with On-Policy Self-Distillation](https://mlsanity.com/paper/2605.15239/) (2026)
- [Learning with Rare Success but Rich Feedback via Reflection-Enhanced Self-Distillation](https://mlsanity.com/paper/2605.12741/) (2026)
- [UniSD: Towards a Unified Self-Distillation Framework for Large Language Models](https://mlsanity.com/paper/2605.06597/) (2026)
- [Latent On-Policy Self-Distillation](https://mlsanity.com/paper/2608.13040/) (2026)
- [PBSD: Privileged Bayesian Self-Distillation for Long-Horizon Credit Assignment](https://mlsanity.com/paper/2606.09348/) (2026)
- [Consensus as Privileged Context for Label-Free Self-Distillation](https://mlsanity.com/paper/2607.13643/) (2026)
- [CriPO: Enhancing Rubric-based RL via Self-Distillation](https://mlsanity.com/paper/2607.18082/) (2026)
- [RISE: Recursive Improvement via Self-Extrapolating Policy Distillation](https://mlsanity.com/paper/2609.05295/) (2026)
- [Learning from the Near Future: Temporal Self-Distillation for RLVR](https://mlsanity.com/paper/2604.20733/) (2026)
- [Why Does Feedback-Augmented Self-Distillation Fail to Improve Retrieval-Interleaved Search Agents?](https://mlsanity.com/paper/2607.17558/) (2026)
- [I-SDPO: Instance-Level Adaptive Self-Distillation Policy Optimization](https://mlsanity.com/paper/2608.12957/) (2026)
- [Future Policy Approximation for Offline Reinforcement Learning in LLM Reasoning](https://mlsanity.com/paper/2509.19893/) (2025)
- [Distilling LLM Feedback for Lean Theorem Proving](https://mlsanity.com/paper/2605.30861/) (2026)
- [Adaptive Supervised Anchoring for On-Policy Self-Distillation](https://mlsanity.com/paper/2608.07935/) (2026)

## Abstract (arXiv)

On-policy self-distillation (OPSD) improves large language models by letting a self-teacher with privileged information provide dense token-level supervision on the model's own trajectories. Yet existing methods typically construct the self-teacher from the current, initial, or slowly averaged policy state, leaving the quality of supervision constrained by the teacher's ability to exploit privileged information. We ask whether the model's own optimization progress can instead be recycled into a stronger self-teacher. In this paper, we introduce Bootstrapped On-Policy Self-Distillation (B-OPSD), which temporarily trains the policy ahead to obtain a future teacher, restores the student to the original policy state, and then uses the future teacher to supervise the restarted student. The future teacher improves supervision in two complementary ways, it can generate more reliable privileged trajectories and, conditioned on them, provide more informative token-level targets along the restarted student's on-policy trajectories. Experiments on mathematical reasoning with Qwen3-4B and Qwen3-8B show consistent improvements over standard OPSD in both settings, including gains from 27.50 to 41.30 and from 48.80 to 64.44 in the rollout-privileged setting. Our findings point to a broader principle for self-improving models that future learning progress can be distilled backward, preserving acquired knowledge while bootstrapping beyond the optimization state that produced it.