Large language models are increasingly used as scalable evaluators for open-ended tasks. However, many LLM judges derive query-specific criteria during scoring, leaving the evaluation requirements insufficiently specified and their coverage difficult to audit. Query-specific rubrics make these requirements explicit, but expert-written rubrics are costly to construct, while existing automatic methods typically rely on inference-time refinement or external supervision. We introduce GenRubric, a self-evolving framework that improves rubric generation from unlabeled queries without requiring additional human annotations during self-evolution. Our approach is based on rubric-induced self-consistency: independently sampled rubrics for the same query provide partial views of its latent evaluation requirements, and a comprehensive rubric should induce a response that generalizes across these complementary evaluation views. We implement this principle through reinforcement learning, combining a cross-rubric comprehensiveness signal with group-level and criterion-level rewards for rubric quality. We train GenRubric models at 4B, 8B, and 14B scales across multiple domains. Experiments on human-annotated rubric benchmarks show that self-evolution improves the agreement between evaluations induced by generated rubrics and those induced by expert-written rubrics. The improvements further generalize to held-out domains, demonstrating the potential of self-evolving rubric generation for scalable and query-specific LLM evaluation. Code and models are publicly available at https://github.com/foggpoy/GenRubric.

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