Correcting or Continuing? What On-Policy Distillation Learns from Student Errors

The paper investigates on‑policy distillation (OPD), a method that trains a student model using its own rollouts while a teacher remains frozen, to see if it can help a student improve on problems it currently fails. Experiments with Qwen‑3 and Phi‑4 models on a competition‑mathematics benchmark show that OPD actually degrades performance when training focuses on failure cases, even though training loss (KL divergence) continues to drop. However, when OPD is applied to a broader set of problems, it improves accuracy by 4.6 percentage points, indicating that OPD works well when most training data contains correct student prefixes but can reinforce errors if the training regime concentrates on failures.

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