Learning Dynamics of On-policy Distillation

On-policy distillation (OPD) is emerging as an important paradigm for language-model post-training, combining dense teacher supervision with training on student-generated trajectories. This creates a feedback loop where each update changes the student and thereby the training distribution that generates subsequent updates. Yet, how this feedback shapes learning and generalization remains poorly understood. We conduct a mechanistic analysis of OPD's learning dynamics, distinguishing the two feedback loop stages: conversion of the distillation signal into parameter updates, and broadcast through which these updates change predictions across prefixes and reshape the rollout distribution. This framework helps explain both limited student responsiveness despite substantial teacher-student disagreement, and degeneration when updates that improve local teacher agreement also increase the probability of unsuccessful continuations, exposing the student to unreliable supervision in subsequent rollouts. Finally, we show that offline distillation can prepare a student for OPD without significantly improving immediate held-out accuracy. While OPD alone may degrade generation, it can yield substantial accuracy gains after sufficient offline preparation. Together, our results connect teacher supervision, student geometry, and the evolving rollout distribution in determining the learning dynamics of OPD and its effects on downstream performance.