Xinlei Yu and coauthors from NUS, MMLab CUHK, PKU, Explore Academy, and JD describe DOPD, a dual on-policy distillation method for LLMs and VLMs. The paper says ordinary privileged distillation can create a privilege illusion, where the student learns to mimic an information advantage it will not have at inference time. Their retained abstract and figure claim gains over several OPD variants on benchmarks including AIME25, LCBv5, MathVision, MMMU-Pro, MATH500, BFCLv3, RealWorldQA, and LiveBench.