On-Policy Delta Distillation

2026-07-16

AI Summary

This work addresses the limitation of traditional on-policy distillation, which relies solely on a teacher model’s output distribution and struggles to effectively transfer reasoning capabilities. To overcome this, the authors propose a novel distillation reward signal—termed the delta signal—that captures the token-level discrepancy between a teacher model and its pre-instruction-tuning base model. This difference precisely isolates the source of enhanced reasoning ability introduced by fine-tuning and serves as the reward objective in reinforcement learning. By incorporating the differential information between pre- and post-fine-tuned models into the on-policy distillation framework for the first time, the method directly targets the essential changes underlying improved reasoning. Experiments demonstrate that this approach significantly outperforms existing distillation strategies across mathematical, scientific, and code reasoning benchmarks, achieving strong performance with only brief post-training.

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

Problem

• on-policy distillation
• reasoning capability
• delta signal
• reinforcement learning
• language models

Innovation

• on-policy distillation
• delta signal
• reasoning capability
• reward-free learning
• knowledge distillation