# Step-Level On-Policy Distillation: Interpolating Between On-Policy Distillation and Supervised Fine-Tuning

arXiv: https://arxiv.org/abs/2608.16333 · HTML: https://mlsanity.com/paper/2608.16333/

## Key facts

- Cited by 8 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 22 of its 24 references that are in the map.
- First posted on arXiv 17 Aug 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, 22 of 22)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [ALFWorld: Aligning Text and Embodied Environments for Interactive Learning](https://mlsanity.com/paper/2010.03768/) (2020)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Sequence-Level Knowledge Distillation](https://mlsanity.com/paper/1606.07947/) (2016)
- [Self-Distilled Reasoner: On-Policy Self-Distillation for Large Language Models](https://mlsanity.com/paper/2601.18734/) (2026)
- [Policy Distillation](https://mlsanity.com/paper/1511.06295/) (2015)
- [OpenThoughts: Data Recipes for Reasoning Models](https://mlsanity.com/paper/2506.04178/) (2025)
- [MathArena: Evaluating LLMs on Uncontaminated Math Competitions](https://mlsanity.com/paper/2505.23281/) (2025)
- [DeepMath-103K: A Large-Scale, Challenging, Decontaminated, and Verifiable Mathematical Dataset for Advancing Reasoning](https://mlsanity.com/paper/2504.11456/) (2025)
- [Learning beyond Teacher: Generalized On-Policy Distillation with Reward Extrapolation](https://mlsanity.com/paper/2602.12125/) (2026)
- [Black-Box On-Policy Distillation of Large Language Models](https://mlsanity.com/paper/2511.10643/) (2025)
- [TCOD: Exploring Temporal Curriculum in On-Policy Distillation for Multi-turn Autonomous Agents](https://mlsanity.com/paper/2604.24005/) (2026)
- [Agent-RLVR: Training Software Engineering Agents via Guidance and Environment Rewards](https://mlsanity.com/paper/2506.11425/) (2025)
- [On-Policy Distillation with Curriculum Turn-level Guidance for Multi-turn Agents](https://mlsanity.com/paper/2606.15912/) (2026)
- [SOD: Step-wise On-policy Distillation for Small Language Model Agents](https://mlsanity.com/paper/2605.07725/) (2026)
- [Imitation Learning for Multi-turn LM Agents via On-policy Expert Corrections](https://mlsanity.com/paper/2512.14895/) (2025)
- [StepOPSD: Step-Aware Online Preference Self-Distillation for Agent Reinforcement Learning](https://mlsanity.com/paper/2605.27140/) (2026)
- [Trajectory-Refined Distillation](https://mlsanity.com/paper/2606.08432/) (2026)
- [Multi-Turn On-Policy Distillation with Prefix Replay](https://mlsanity.com/paper/2607.04763/) (2026)
- [SAF-OPD: Stable Advantage Fusion for On-Policy Distillation](https://mlsanity.com/paper/2607.29209/) (2026)

## Built on by (most cited first, 8 of 8)

- [On the Off-Policy Teacher in On-Policy Distillation](https://mlsanity.com/paper/2609.38360/) (2026)
- [GraphOPD: Graph-Augmented On-Policy Distillation for LLM Agents](https://mlsanity.com/paper/2610.08959/) (2026)
- [SAPD: Step-Aligned Privileged Distillation](https://mlsanity.com/paper/2610.09665/) (2026)
- [State-OPD: State-Grounded On-Policy Distillation for Multi-Turn Agents](https://mlsanity.com/paper/2610.13238/) (2026)
- [Beyond Domain-Routed Supervision: Cross-Teacher Guarding for Multi-Teacher On-Policy Distillation](https://mlsanity.com/paper/2610.13521/) (2026)
- [JustOPD: On-Policy Distillation from Autoregressive to Diffusion Language Models](https://mlsanity.com/paper/2610.17397/) (2026)
- [DTDD: Divergence-Triggered Dynamic Distillation for Reliable On-Policy Supervision](https://mlsanity.com/paper/2610.19302/) (2026)
- [Beyond Corrected Actions: Training LLM Agents on Textual Critiques](https://mlsanity.com/paper/2610.19367/) (2026)

## Abstract (arXiv)

On-policy distillation (OPD) aligns a student model with a teacher's logit distribution on student-generated trajectories. This approach has achieved strong empirical gains and can often surpass conventional off-policy distillation with substantially less data. However, standard token-level OPD can provide only fragmented corrections along an erroneous student trajectory and cannot unfold a complete and correct repair path. Motivated by this limitation, we propose Step-Level On-Policy Distillation (SOPD), which combines the long-horizon correction of supervised fine-tuning (SFT) with the on-policy advantage of OPD to provide step-level supervision over complete student-generated trajectories. We show that, at different limits of step length, SOPD reduces to SFT or approximates OPD. Compared with SFT, the teacher responses in SOPD are conditioned on student trajectories and therefore align more closely with student-visited states; compared with OPD, SOPD provides longer-horizon corrections rather than fragmented token-level guidance. Across both reasoning and agent tasks, SOPD substantially outperforms conventional SFT and OPD. For example, on ALFWorld, SOPD improves the average success rate by 13.4 points over Vanilla OPD. We hope this work offers a new perspective for future research on distillation methods.