Generative recommendation retrieves items by autoregressively generating semantic IDs, typically via beam search. On-policy self-distillation (OPSD) enhances training supervision by transferring privileged self-teacher knowledge at student-generated states. However, beam-search retention depends on competition among prefixes: visited states differ in importance, and initially reliable decisions may approach the pruning boundary as training evolves. Moreover, conventional distribution matching couples target-token confidence with preferences among competing continuations, potentially weakening relational supervision when the self-teacher strongly favors the target. To address these challenges, we propose Search-Aware On-Policy Self-Distillation (SA-OPSD), a framework that transfers privileged self-teacher knowledge to the states visited during the student's own beam search. Specifically, we introduce Evolving-Boundary Sampling, which prioritizes search-critical states by considering both current pruning-boundary proximity and initial-reference retention-margin decline under a controlled distillation budget. Furthermore, we develop Confidence-Decoupled Branch Distillation, which separates target-probability calibration from informative sibling relations to better preserve the teacher's preferences among competing branches. Experiments on Industrial, Office, and Instruments demonstrate strong performance for SA-OPSD.

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