DTDD: Divergence-Triggered Dynamic Distillation for Reliable On-Policy Supervision

Qijia He, Zequn Li, Spencer Luo, Tianle Chen, Pradyumna Narayana +4

On-policy distillation (OPD) provides dense token-level supervision on student rollouts, but this supervision can become unreliable when the student and teacher diverge, either because of a large initial policy gap or compounding errors in long-horizon reasoning and tool use. We introduce Divergence-Triggered Dynamic Distillation (DTDD), an adaptive OPD framework that uses segment-level student-teacher divergence to trigger teacher takeover during training. When divergence triggers an intervention during reasoning, the student prefix continues to receive standard OPD supervision. The teacher then generates a recovery suffix, which the student learns through behavior cloning, using cross-entropy on the teacher-generated tokens. We evaluate DTDD in three regimes: long-horizon reasoning, distillation from a base initialization without offline supervised fine-tuning (SFT), and multi-turn agents. We also compare alternative trigger designs and teacher-intervention rates. DTDD reduces the post-warmup peak gradient norm by $8.6\times$ and, from a base initialization, reaches $21.3\%$ held-out math accuracy in $2.6\times$ fewer optimizer updates than OPD; both methods finish near $22\%$.…