Calibrating Teacher–Student Discrepancy for On-Policy Distillation

On-policy distillation (OPD) improves reasoning models by learning the token-level discrepancy between a stronger teacher and an on-policy student. However, this discrepancy does not purely reflect the capability gap between the teacher and the student: it also contains deviations arising from the teacher itself, which are consequently mixed into the observed teacher–student discrepancy and indiscriminately learned by standard OPD during training. This issue is further exacerbated by privileged OPD, where privileged information induces larger teacher-side likelihood shifts, thereby encouraging the student to learn more of the teacher's own deviation. We introduce Calibrated On-Policy Distillation (Cal-OPD), which estimates the teacher's self-deviation region through positive and negative privileged interventions and calibrates the original teacher–student discrepancy by retaining only the component that lies beyond this region. Experiments on mathematical reasoning benchmarks show that, while retaining only about 52–65% of the original teacher–student discrepancy as the optimization signal, Cal-OPD consistently outperforms standard OPD and its variants across model scales.