Ask to Distill: Learning to Synthesize Data for On-Policy Distillation

Jiashuo Sun, Hao Zhang, Xueqiang Xu, Heng Wang, Yixuan Xie +7

On-policy distillation (OPD) can succeed with surprisingly few training questions, motivating a view of questions as carriers of distributional knowledge transfer. How can we assess whether a newly generated question is valuable for distillation, and learn to generate better questions---without access to its correct answer? We introduce Ask-to-Distill (\method), a framework that treats synthetic questions as distribution elicitors and optimizes the teacher supervision they expose along student-generated trajectories. A student-initialized synthesizer is optimized using a distributional surrogate for question value, computed from a frozen student--teacher pair without reference answers, correctness rewards, or per-candidate student updates. The reward combines teacher--student disagreement with teacher probability mass on the student's candidate support, together with length and diversity controls. The generated questions are filtered and deduplicated into a prompt-only bank for standard OPD. Across mathematical reasoning, code generation, and agentic tasks, our method improves average performance and teacher-gap recovery over unoptimized student-generated prompts and KL-filtered…