The Many Faces of On-Policy Distillation: Pitfalls, Mechanisms, and Fixes

TL;DR

This paper provides a comprehensive empirical analysis of on-policy distillation methods for large language models, identifying their strengths, failure modes, and proposing mitigation strategies.

Contribution

It systematically investigates when on-policy distillation works or fails, and introduces techniques to address identified failure mechanisms.

Findings

OPD on mathematical reasoning is sensitive to teacher choice.

OPSD fails without instance-specific privileged information.

Mitigation strategies include stop-gradient TopK and RLVR-adapted teachers.

Abstract

On-policy distillation (OPD) and on-policy self-distillation (OPSD) have emerged as promising post-training methods for large language models, offering dense token-level supervision on trajectories sampled from the model's own policy. However, existing results on their effectiveness remain mixed: while OP(S)D has shown promise in system prompt and knowledge internalization, recent studies also report instability and degradation. In this work, we present a comprehensive empirical study of when OPD and OPSD work, when they fail, and why. We find that OPD on mathematical reasoning is highly sensitive to teacher choice and loss formulation, whereas OPSD fails in our tested settings due to test-time absence of instance-specific privileged information (PI). In contrast, OPSD is effective when PI represents a shared latent rule, such as a system prompt or alignment preference. We identify three failure mechanisms: (1) distribution mismatch between teacher and student caused by conditioning on student-generated prefixes, (2) optimization instability from biased TopK reverse-KL gradients, and (3) an OPSD-specific limitation where the student learns a PI-free policy that aggregates PI-conditioned teachers, which is insufficient when PI is instance-specific. We further show that stop-gradient TopK objectives, RLVR-adapted teachers, and SFT-stabilized students mitigate these failures.