# Stable On-Policy Distillation through Adaptive Target Reformulation

arXiv: https://arxiv.org/abs/2601.07155 · HTML: https://mlsanity.com/paper/2601.07155/

## Key facts

- Cited by 53 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 16 of its 19 references that are in the map.
- First posted on arXiv 12 Jan 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, 16 of 16)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Scheduled Sampling for Sequence Prediction with Recurrent Neural Networks](https://mlsanity.com/paper/1506.03099/) (2015)
- [Sequence-Level Knowledge Distillation](https://mlsanity.com/paper/1606.07947/) (2016)
- [WizardCoder: Empowering Code Large Language Models with Evol-Instruct](https://mlsanity.com/paper/2306.08568/) (2023)
- [Sequence Level Training with Recurrent Neural Networks](https://mlsanity.com/paper/1511.06732/) (2015)
- [DialogSum: A Real-Life Scenario Dialogue Summarization Dataset](https://mlsanity.com/paper/2105.06762/) (2021)
- [Bridging the Gap between Training and Inference for Neural Machine Translation](https://mlsanity.com/paper/1906.02448/) (2019)
- [f-Divergence Minimization for Sequence-Level Knowledge Distillation](https://mlsanity.com/paper/2307.15190/) (2023)
- [Why Exposure Bias Matters: An Imitation Learning Perspective of Error Accumulation in Language Generation](https://mlsanity.com/paper/2204.01171/) (2022)
- [Speculative Knowledge Distillation: Bridging the Teacher-Student Gap Through Interleaved Sampling](https://mlsanity.com/paper/2410.11325/) (2024)
- [Autoregressive Knowledge Distillation through Imitation Learning](https://mlsanity.com/paper/2009.07253/) (2020)
- [Relating Neural Text Degeneration to Exposure Bias](https://mlsanity.com/paper/2109.08705/) (2021)

## Built on by (most cited first, 30 of 53)

- [Rethinking On-Policy Distillation of Large Language Models: Phenomenology, Mechanism, and Recipe](https://mlsanity.com/paper/2604.13016/) (2026)
- [A Survey of On-Policy Distillation for Large Language Models](https://mlsanity.com/paper/2604.00626/) (2026)
- [Uni-OPD: Unifying On-Policy Distillation with a Dual-Perspective Recipe](https://mlsanity.com/paper/2605.03677/) (2026)
- [TCOD: Exploring Temporal Curriculum in On-Policy Distillation for Multi-turn Autonomous Agents](https://mlsanity.com/paper/2604.24005/) (2026)
- [Filter, Then Reweight: Rethinking Optimization Granularity in On-Policy Distillation](https://mlsanity.com/paper/2606.02684/) (2026)
- [Prune-OPD: Efficient and Reliable On-Policy Distillation for Long-Horizon Reasoning](https://mlsanity.com/paper/2605.07804/) (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)
- [Decoupling KL and Trajectories: A Unified Perspective for SFT, DAgger, Offline RL, and OPD in LLM Distillation](https://mlsanity.com/paper/2605.16826/) (2026)
- [MAD-OPD: Breaking the Ceiling in On-Policy Distillation via Multi-Agent Debate](https://mlsanity.com/paper/2605.01347/) (2026)
- [TurnOPD: Making On-Policy Distillation Turn-Aware for Efficient Long-Horizon Agent Training](https://mlsanity.com/paper/2607.05804/) (2026)
- [Trajectory-Refined Distillation](https://mlsanity.com/paper/2606.08432/) (2026)
- [SimCT: Recovering Lost Supervision for Cross-Tokenizer On-Policy Distillation](https://mlsanity.com/paper/2605.07711/) (2026)
- [DOPD: Dual On-policy Distillation](https://mlsanity.com/paper/2606.30626/) (2026)
- [OPRD: On-Policy Representation Distillation](https://mlsanity.com/paper/2606.06021/) (2026)
- [Escaping the KL Agreement Trap in On-Policy Distillation](https://mlsanity.com/paper/2606.09471/) (2026)
- [Prefix-Guided On-Policy Distillation: Mining Golden Trajectories from Rollouts](https://mlsanity.com/paper/2606.21994/) (2026)
- [PowerOPD: Stabilizing On-Policy Distillation with Bounded Power Transformation](https://mlsanity.com/paper/2606.17199/) (2026)
- [Trust-Region Behavior Blending for On-Policy Distillation](https://mlsanity.com/paper/2605.31159/) (2026)
- [Weak-to-Strong On-Policy Distillation](https://mlsanity.com/paper/2607.26246/) (2026)
- [ORBIT: On-policy Exploration-Exploitation for Controllable Multi-Budget Reasoning](https://mlsanity.com/paper/2601.08310/) (2026)
- [On-Policy Distillation with Best-of-N Teacher Rollout Selection](https://mlsanity.com/paper/2605.09725/) (2026)
- [A Formula-Driven Survey and Research Agenda for On-Policy Distillation](https://mlsanity.com/paper/2606.22793/) (2026)
- [DemoPSD: Disagreement-Modulated Policy Self-Distillation](https://mlsanity.com/paper/2607.02502/) (2026)
- [ADWIN: Adaptive Windows for Horizon-Aware On-Policy Distillation](https://mlsanity.com/paper/2605.28396/) (2026)
- [RISE: Recursive Improvement via Self-Extrapolating Policy Distillation](https://mlsanity.com/paper/2609.05295/) (2026)
- [Z-Reward: Beyond Scalar Rewards by Internalizing Reasoning into Score Distributions](https://mlsanity.com/paper/2606.09076/) (2026)
- [Simple-OPD: Demystifying Warm-up for On-policy Distillation](https://mlsanity.com/paper/2608.06802/) (2026)
- [Beyond Absolute Imitation: Anchored Residual Guidance for Privileged On-Policy Distillation](https://mlsanity.com/paper/2606.10385/) (2026)
- [Trust Region Policy Distillation](https://mlsanity.com/paper/2607.04751/) (2026)

## Abstract (arXiv)

Knowledge distillation (KD) is a widely adopted technique for transferring knowledge from large language models to smaller student models; however, conventional supervised KD often suffers from a distribution mismatch between training and inference. While on-policy KD approaches attempt to mitigate this issue by learning directly from student-generated outputs, they frequently encounter training instabilities because the distributional gap between the novice student and the expert teacher is often too wide to bridge directly. These challenges manifest as pathological gradients in forward KL objectives or diversity collapse in reverse KL regimes. To address these limitations, we propose Veto, an objective-level reformulation that constructs a geometric bridge in the logit space. Unlike prior methods that mix data samples, Veto creates an intermediate target distribution that promotes alignment between the teacher and the student. By introducing a tunable parameter beta, Veto serves as an Adaptive Gradient Veto that stabilizes optimization by suppressing harmful gradients on low-confidence tokens, while simultaneously acting as a Decisiveness Knob to balance reward-driven performance with output diversity. Extensive experiments across various reasoning and generation tasks demonstrate that Veto consistently outperforms supervised fine-tuning and existing on-policy baselines.