Diffusion large language models (dLLMs) generate text in parallel through iterative denoising and are considered a new path beyond autoregressive (AR) LMs, but the post-training phase for strong reasoning has been awkward — supervised fine-tuning is off-policy and suffers from exposure bias, reinforcement learning only has sparse whole-sentence rewards, and because dLLMs lack tractable sequence likelihoods, it's hard to directly apply standard methods. The dOPSD (arXiv 2607.04428) posted to arXiv on July 5 by NUS's Phuong Tuan Dat, Qi Li, and Xinchao Wang goes straight at this pit. The paper first points out that On-Policy Self-Distillation (OPSD) was originally a beautiful-looking path: the same model serves as both student and teacher, providing dense, token-level, on-policy supervision signals. But OPSD's key pain point is that the teacher must obtain "privileged information" (PI) — usually a sample-level ground truth, completely unavailable at inference time, so the student only learns a weak consensus policy with PI removed, which is almost no help for dLLM reasoning. dOPSD's core idea: the teacher's privilege no longer comes from external labels, but from the later part of the student's own denoising trajectory — the later steps have "decoded deeper" than the front, naturally serving as superior soft labels for the masked positions. The teacher's advantage is thus entirely grown from the model's own decoding process, requiring no extra signals at deployment. The paper applies dOPSD to two representative dLLMs, Dream and LLaDA, and the results simultaneously exceed SFT and existing on-policy baselines on in-domain math reasoning and out-of-domain code generation. For the dLLM community that's intensely iterating on post-training, this is essentially decoupling the two most expensive costs — "where does the data come from" and "where do the labels come from" — and the next step of porting this idea to multimodal diffusion LLMs is almost a ready-made direction.