COPD is proposed, a contrastive OPD framework that substantially reduces reasoning length without compromising model performance and consistently improves efficiency across different tasks and model scales.
Abstract
On-policy Distillation (OPD) supervises a student model on trajectories sampled from its own policy by minimizing the divergence between the output distributions of the teacher and student at each token position, thereby providing dense token-level supervision. Although existing OPD methods have demonstrated strong performance in improving the reasoning ability of student models, their objectives fundamentally rely on token-level distribution matching. Consequently, they lack an explicit signal for comparing a token's relative compatibility across reasoning modes and thus do not directly model preferences between these modes. To address this limitation, we propose COPD, a contrastive OPD framework. Specifically, for each token generated by the student model, a frozen teacher model scores the same student state under two contrasting instructions that elicit light and heavy reasoning. The difference between the resulting log probabilities serves as a token-level advantage signal to guide the OPD update. Rather than merely imitating a single teacher distribution, COPD directly encourages the student model to learn more concise and efficient reasoning strategies. We conduct experiments on nine multimodal benchmarks covering both reasoning and understanding tasks. The results show that COPD substantially reduces reasoning length without compromising model performance and consistently improves efficiency across different tasks and model scales. Furthermore, the contrastive formulation can be seamlessly integrated into the On-policy Self-distillation (OPSD) framework, where self-contrastive supervision is constructed without an additional teacher model, thereby enabling the model to distill itself toward lightweight reasoning.
On-policy distillation (OPD) trains a student on its own trajectories while a teacher supplies dense token-level likelihoods at student-visited prefixes. These likelihoods are often read locally: agreement appears safe to imitate, whereas disagreement appears to identify an error. We show that both readings are confounded by the outcome of the completed trajectory. We introduce an outcome-resolved diagnostic that crosses pointwise teacher-student divergence with final-answer correctness, separating safe imitation, productive divergence, harmful divergence, and agreement-on-failure. In an eight-seed mathematical-reasoning study with a Qwen3-8B student and Qwen3-32B teacher, agreement-on-failure constitutes 67.84% of pooled response-token mass; with a Qwen2.5-7B/32B pair it remains 67.68%. The result persists across threshold, sequence-level, format, and truncation audits. Even on prompts that the Qwen3 teacher solves in all four independent attempts, student accuracy rises to 86.91% but agreement-on-failure remains 14.76%. We then run three matched training probes that use the available signals to imitate, mask, or contrast whole trajectories; none consistently reduces agreement-on-failure. The result points to a localization limitation: local divergence paired with a trajectory-level outcome does not identify where a failed trajectory became unrecoverable. Addressing this limitation requires additional positional information, such as process labels, teacher continuations from student prefixes, or token-level alignment across rollouts. Our contribution is therefore diagnostic rather than a new training method.
On-policy distillation (OPD), which aligns a student with the teacher's token-level distribution on the student's own rollouts, is an effective paradigm for transferring capabilities across LLMs. Prevailing approaches assume a teacher at least as capable as the student: they either distill a larger model into a smaller one, which fails at the frontier where no larger teacher exists, or consolidate multiple domain experts trained from a shared base, which requires costly training at the student's scale. We introduce Weak-to-Strong On-Policy Distillation (W2S-OPD), a simple yet effective OPD framework that improves the strong student by distilling from multiple weak models. W2S-OPD constructs a proxy teacher in logit space from a contrast pair of a positive and a negative model, both smaller than the student and cheap to obtain. Their logit difference isolates the capability direction, which is added to the student's own base model, yielding a proxy teacher that couples this direction while staying distributionally adjacent to the student. The student then distills it by minimizing the per-token reverse KL on its own rollouts. We instantiate the contrast pair as i) a post-RL expert against its pre-RL initialization, isolating the skill RL instills, ii) a larger against a smaller base model, isolating the capability from scale, and iii) a small base model with correct versus wrong hints, isolating the instance-level direction toward the solution. Across four math and three code benchmarks, W2S-OPD outperforms OPD, enables the student to surpass the domain teacher, and keeps improving the student even when every supervision source is weaker. Analysis shows different contrasts yield distinct signals: the post-RL and hint contrasts emphasize reasoning frameworks, while the scale contrast emphasizes the solving procedure. Our code will be available at https://github.com/Yu-Fangxu/W2S-OPD.
Fangxu Yu, Zinan Lin, Xiaodong Liu et al.· arXiv.org· 6 citations· ⚡1
This work proposes Reasoning-Progress-Aware Reward Filtering for On-Policy Distillation (R2-OPD), which constructs two within-trajectory rankings of reasoning spans, one from teacher-derived rewards and the other from independently estimated progress reward.
Chen Yang, Hai-Yuan Wan, Rengrong Xiong et al.· 0 citations
On-policy distillation (OPD) aligns a student model with a teacher's logit distribution on student-generated trajectories. This approach has achieved strong empirical gains and can often surpass conventional off-policy distillation with substantially less data. However, standard token-level OPD can provide only fragmented corrections along an erroneous student trajectory and cannot unfold a complete and correct repair path. Motivated by this limitation, we propose \emph{Step-Level On-Policy Distillation} (SOPD), which combines the long-horizon correction of supervised fine-tuning (SFT) with the on-policy advantage of OPD to provide step-level supervision over complete student-generated trajectories. We show that, at different limits of step length, SOPD reduces to SFT or approximates OPD. Compared with SFT, the teacher responses in SOPD are conditioned on student trajectories and therefore align more closely with student-visited states; compared with OPD, SOPD provides longer-horizon corrections rather than fragmented token-level guidance. Across both reasoning and agent tasks, SOPD substantially outperforms conventional SFT and OPD. For example, on ALFWorld, SOPD improves the average success rate by 13.4 points over Vanilla OPD. We hope this work offers a new perspective for future research on distillation methods.
Changhui Sun, Lan-Bo Liu, Hang Lei et al.· 0 citations
This review treats collapse as a symptom governed by three levers: where the signal is applied, that is, how tokens are weighted; what the teacher is shown, that is, the nature of the privileged information; and when the signal changes, that is, the teacher's dynamics and the decay of guidance.
It is found that learning concentrates on low log-probability tokens, and using a single fixed negative advantage matches the performance of teacher-provided ones, suggesting that OPD works largely by suppressing low log-probability tokens, which requires no teacher.
Yi Ding, Ruqi Zhang· 0 citations
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