arxiv:2607.15161

On-Policy Delta Distillation

Published on Jul 16

· Submitted by

Byeongho Heo on Jul 20

NAVER AI Lab

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Authors:

Byeongho Heo ,

Jaehui Hwang ,

Sangdoo Yun ,

Dongyoon Han

Abstract

On-policy distillation is an alternative post-training method in reinforcement learning that alleviates the constraints imposed by reward models by providing token-level supervision from a teacher model. Although on-policy distillation has been studied and applied across various settings, its fundamental design remains underexplored. In this paper, we introduce a new distillation reward, termed the delta signal, instead of directly imitating the teacher's output distribution. The delta signal is defined as the difference between the teacher model and its base model prior to instruction tuning for reasoning capability. It therefore captures the changes induced by reasoning tuning and provides a more direct signal for transferring reasoning capabilities. Using extensive empirical evidence, we show that the delta signal substantially improves on-policy distillation and refer to the new distillation method as On-Policy Delta Distillation (OPD^2). Experiments across mathematics, science, and code-reasoning benchmarks demonstrate that OPD^2 consistently outperforms conventional on-policy distillation, enabling reasoning LLMs to achieve strong performance with only a short post-training period. Code will be available at https://github.com/naver-ai/opd2

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bhheo

Paper author Paper submitter 2 days ago

We introduce On-Policy Delta Distillation (OPD²), which uses the difference between a reasoning-tuned teacher and its base model as the distillation signal. By focusing on the capability gained during reasoning tuning, OPD² consistently improves on-policy distillation across math, science, and code. The gains hold across multiple Qwen3 model sizes, in both thinking and non-thinking modes, and generalize beyond Qwen3 to Gemma 4.

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about 19 hours ago

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Ma-Vector

about 18 hours ago

This seems closely connected to Direct-OPD. OPD² uses

$\Delta_t=\log\pi_{\mathrm{teacher}}(y_t|h_t)-\log\pi_{\mathrm{base}}(y_t|h_t),$

while Direct-OPD shows that, under KL-regularized RL, the log-ratio between a post-training policy and its reference policy recovers the implicit reward up to scaling and a context-dependent constant.

Therefore, when the reasoning teacher is obtained by post-training the base teacher, the OPD² delta can be interpreted as the dense implicit reward encoded by that post-training process. In this sense, Direct-OPD provides a theoretical explanation for why distilling the teacher–base delta may be more effective than directly imitating the final teacher: the delta isolates the learned policy shift while cancelling much of the base model’s original prior.

The settings are not completely identical, since Direct-OPD specifically analyzes RL-induced shifts, whereas OPD² also considers broader reasoning tuning. Still, both papers appear to instantiate the same principle: transfer the update introduced by post-training, rather than the final model distribution itself.

bhheo

Paper author about 15 hours ago

Thank you for the clarification. We agree that OPD² and Direct-OPD share a closely related underlying principle, while each makes distinct contributions due to differences in setting and purpose. We will consider discussing Direct-OPD as concurrent related work in a future revision.