Teach Me After You Learn It: Lookahead Self-Distillation for RLVR

On-policy self-distillation (OPSD) has emerged as a popular training paradigm for LLMs, providing dense, token-level supervision by aligning a model's own distribution with the distribution induced by privileged information. However, existing OPSD methods derive supervision solely from privileged information of the same instance, leaving inter-instance supervision largely unexplored. We propose Lookahead Self-Distillation (LEAD), which introduces inter-instance distillation by allowing the teacher to first learn from other on-policy rollouts before teaching the student. LEAD constructs lookahead teachers through virtual RL updates on disjoint subsets of on-policy rollouts, and uses each teacher to provide cross-group token-level supervision for the other subset. To reconcile the complementary yet potentially conflicting signals from OPSD and RLVR, we introduce harmonious modulation, which adaptively modulates the GRPO advantage based on the agreement between the two signals. Extensive experiments on scientific reasoning and interactive-agent benchmarks show that LEAD achieves the best in-domain average performance across model scales while maintaining out-of-domain generalization comparable to GRPO.