Modern retrieval systems increasingly require filtered vector search under arbitrary predicate constraints, where users filter results by attributes such as category, price, location, keywords, and their combinations. Existing solutions either specialize in a single predicate type (e.g., range or equality filters), rely on dense, high-overhead indexes, or fail to handle predicates with diverse selectivities. As a result, they fail to simultaneously achieve efficiency, scalability, and flexibility. In this paper, we propose CGIF, an index that efficiently supports approximate nearest neighbor search (ANNS) both with and without predicates, while preserving the lightweight and scalable structure of the widely adopted vector index HNSW. Our design builds on an observation from previous works that HNSW traversal naturally consists of two phases: (1) a navigation phase, where the search rapidly moves toward the query's vicinity, and (2) a local exploration phase, where traversal expands locally to refine results. CGIF retains the original HNSW search strategy during navigation to efficiently reach the query region, and introduces a predicate-aware traversal during local exploration. When a neighbor does not satisfy the query predicates, CGIF replaces it with alternative candidates drawn via inverted-file (IVF) indexing, ensuring effective local exploration under diverse predicates. Extensive experiments on multiple real-world datasets show that CGIF consistently outperforms state-of-the-art filtered vector search methods, delivering up to 2× faster query performance while maintaining high recall across diverse predicate types and selectivities.
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