Learning from Think-Mode Advantage via On-Policy Distillation

On-policy self-distillation (OPSD) lets a language model learn from a frozen copy of itself that sees an answer or a worked solution. Giving the teacher this extra information seems to offer the student more to learn, but how much does it add beyond distillation itself? To isolate that contribution, we construct AMPLE-Math, a reusable suite of 5,319 mathematical problems with six reasoning views that share the same answer, and compare each view with matched reference-free distillation. With a thinking-enabled teacher supervising direct-response rollouts, reference-free distillation accounts for much of Qwen3-1.7B's improvement under thinking-enabled evaluation, both in domain and on external benchmarks. Evidence for an additional reference benefit is modest in Qwen, strongest for a polished solution, whereas complete traces add two percentage points in SmolLM3-3B at step 50. These benefits depend on the student being trained. At the same checkpoint, replacing short direct-response rollouts with long thinking-enabled rollouts turns gains into losses in both families while the problems, references, and evaluation stay fixed. Teacher profiles and matched loss interventions in Qwen further show that changing token-level supervision can leave student behavior largely unchanged. Together, these findings suggest that OPSD can improve access to existing reasoning capabilities through parameters shared by direct-response and thinking-enabled inference. The value of a privileged reference is what it adds to this cross-mode transfer, not how much of the solution it reveals.

On-Policy Distillation (OPD) improves large language model reasoning by training a student model on trajectories sampled from its own policy under teacher supervision. Although OPD operates on trajectories, its learning signal remains token-level: it identifies deviations through high-loss tokens and repairs them through local reverse-KL correction. We show that this "trajectory-sampled but token-learned" mechanism cannot reliably bridge student trajectories toward teacher trajectories. About 30% of high-loss tokens fall into the low-divergence regime, indicating that many are surface-form mismatches rather than real reasoning forks. Moreover, even truly divergent tokens are difficult to repair with isolated token-level supervision, since reasoning failures often unfold as short-horizon distributional drift. We propose Trajectory-aware OPD (TOPD), which uses near-future trajectory information to identify real divergent states and distribute guidance across multiple future tokens. Experiments show that suppressing non-divergent high-loss tokens improves standard OPD from 47.8% to 48.2% average accuracy, while TOPD further improves performance to 52.2%, with gains on AIME24 from 60.0% to 63.3% and AIME25 from 46.7% to 53.3%.

Self-distillation is a promising recipe for self-improvement in language models. In this setting, a model can serve as its own teacher when given privileged information, such as a solution to a math problem. This seems especially appealing for thinking models, which can use test-time reasoning to absorb the privileged information. Surprisingly, we show that privileged self-distillation degrades thinking models on long reasoning traces: across five Qwen3 and OLMo thinking models evaluated on AIME24, AIME25, and HMMT25, privileged-context distillation causes a relative drop of up to 17% in avg@16 accuracy. The degradation scales with the amount of privileged context withheld from the student and is most pronounced at long rollout budgets, where thinking models otherwise obtain their largest gains. This failure mode is not specific to self-distillation: on-policy distillation (OPD) improves thinking models, but privileged OPD reverses these gains. Our diagnostics link this failure mode to how privileged teacher context reshapes learning at high-entropy forking positions, where multiple continuations remain plausible and may lead to different reasoning paths. Privileged context lowers fork rates in thinking-model rollouts but not in instruction-model rollouts. This leads to an interesting dichotomy, where privileged context can help instruction-tuned models but hurts stronger thinking models. The effect is visible when the student begins a self-correction branch, where privileged OPD penalizes sampled reconsideration tokens that vanilla OPD supports. Thinking models trained with a privileged teacher produce fewer verification, backtracking, and hedging markers, even after length normalization. These findings indicate that self-distillation for strong thinking models requires attention to token-level signal, especially around correction and reasoning steps.