Explicit intermediate reasoning gives large language models (LLMs) a stronger problem-solving mode.
We study learning from this think-mode advantage via on-policy distillation (OPD).
OPD preserves student-generated trajectories and provides dense token-level teacher targets at student-visited prefixes.
Privileged reasoning is used during distillation rather than student inference.
Uniform ThinkOPD, a natural think-enabled OPD baseline, conditions a fixed teacher on one shared think trace and uniformly distills every sibling student response.
Although its prefixes are on-policy, the trace need not follow a route compatible with every complete response: the same privileged trace can induce different teacher-student discrepancies even when responses reach the same outcome.
We summarize this interaction with trace-response divergence (TRD) and introduce ThinkOPD, which routes supervision at the response level by combining group-relative reward gain with a TRD-based compatibility proxy.
Final response weights are normalized within each rollout group.
Across mathematical reasoning and code generation, ThinkOPD outperforms Uniform ThinkOPD in both same-model settings and both cross-model teacher-student pairs, and it exceeds representative rationale and self-distillation baselines in a controlled comparison.
Controlled interventions show that outcome benefit and the TRD-based proxy provide complementary routing signals in this setting.
Think-enabled OPD provides a controlled setting for studying how teacher advantage becomes transferable along student responses.