Faceted search acts as a critical bridge for navigating massive ecommerce catalogs, yet traditional systems rely on static rule-based extraction or statistical ranking, struggling with emerging vocabulary, semantic gaps, and a disconnect between facet selection and underlying retrieval. In this paper, we introduce GenFacet, an industrial-grade, end-to-end generative framework deployed at JD.com. GenFacet reframes faceted search as two coupled generative tasks within a unified Large Language Model: Context-Aware Facet Generation, which dynamically synthesizes trend-responsive navigation options, and Intent-Driven Query Rewriting, which translates user interactions into precise search queries to close the retrieval loop. To bridge the gap between generative capabilities and search utility, we propose a novel multi-task training pipeline combining teacher-student distillation with GRPO. This aligns the model with complex user preferences by directly optimizing for downstream search satisfaction. Validated on China's largest selfoperated e-commerce platform via rigorous offline evaluations and online A/B tests, GenFacet demonstrated substantial improvements. Specifically, online results reveal a relative increase of 42.0% in facet Click-Through Rate (CTR) and 2.0% in User Conversion Rate (UCVR). These outcomes provide strong evidence of the benefits of generative methods for improving query understanding and user engagement in large-scale information retrieval systems.