arXiv Machine Learning By Denis Blessing, Lorenz Richter, Julius Berner, Egor Malitskiy, Gerhard Neumann

Bridge Matching Sampler: Scalable Sampling via Generalized Fixed-Point Diffusion Matching

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Bridge Matching Sampler (BMS) is a new diffusion-based sampling method that generalizes least-squares matching objectives into fixed-point iterations using Nelson's relation. It learns a stochastic transport map between any prior and target distribution with a single, scalable, and stable objective, and a damped variant adds regularization to reduce mode collapse. Experiments show BMS can sample at unprecedented scales while preserving mode diversity, achieving state‑of‑the‑art results on complex synthetic densities and high‑dimensional molecular benchmarks.

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