NAVER AI Lab published "On-Policy Delta Distillation" (arXiv:2607.15161) on arXiv on July 16, providing a more direct, more economical path for distilling large reasoning models in post-training. Authors: Byeongho Heo, Jaehui Hwang, Sangdoo Yun and Dongyoon Han. The traditional on-policy distillation target usually asks the student to directly mimic the teacher's output distribution. But this target inevitably mixes in the teacher's own language priors — the student has to both learn reasoning and bear all of the teacher's pre-existing world priors, which is costly and inefficient. NAVER's core insight: the essence of reasoning ability comes from "the incremental change of the teacher relative to its homologous base model". The paper defines this increment as the delta signal, i.e., "the per-token distribution difference between the teacher and its homologous base model", precisely stripping away the pretraining residue and keeping only "the components newly introduced during instruction tuning or reasoning RL". The OPD² distillation objective, redesigned on the delta signal, consistently outperforms traditional on-policy distillation on math, science and code reasoning benchmarks; the student needs only a very short post-training cycle to approach the teacher's performance. The experimental report covers 19 pages of text, 4 figures and 12 tables, with relatively complete empirical support. Code will be open-sourced at github.com/naver-ai/opd2, and can be plugged into mainstream RL post-training flows afterwards. The deeper meaning of this path: it re-calibrates "what to distill" from "mimic the overall output distribution" to "transfer what the teacher truly learned new during RL/instruction tuning". It continues the past half-year's academic discussion of fine-grained reasoning post-training objectives — from token-level imitation to preference-based RL, to delta-based distillation, with the objective granularity getting finer and finer. For research and engineering teams chasing small models inheriting large-model reasoning ability while controlling training cost, this is one of the few genuinely mechanism-level rather than engineering-level advances in recent months.