Retrieval-augmented generation improves large language models by grounding outputs in external knowledge sources, reducing hallucinations and addressing knowledge cutoffs. However, standard embedding-based retrieval fails to capture the complexity of multi-concept queries, particularly in domains like biomedicine, where biological data are inherently high-dimensional. For example,omics datasets, and clinical reports simultaneously exhibit numerous molecular, cellular, and physiological features. We present Stochastic Latent Matching (STHLM), a generative vector search method that samples query-conditioned embeddings from text or image inputs to enhance retrieval performance. Analogous to how Chain-of-Thought reasoning enables language models to "think longer" on complex problems, STHLM allows retrieval systems to "search wider" through iterative sampling. STHLM demonstrates critical improvements over classical vector retrieval across diverse benchmarks, including scientific literature, clinical notes, and tissue images, boosting retrieval performance by 10-30% through test-time compute (trading latency for accuracy), while enabling up to a 10-fold compression of embedding dimensions.