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

• URL: http://arxiv.org/abs/2603.00530v1
• Date: Sat, 28 Feb 2026 08:00:38 GMT
• Title: Bridge Matching Sampler: Scalable Sampling via Generalized Fixed-Point Diffusion Matching
• Authors: Denis Blessing, Lorenz Richter, Julius Berner, Egor Malitskiy, Gerhard Neumann,
• Abstract summary: Bridge Matching Sampler (BMS) enables learning a transport map between arbitrary prior and target distributions with a single, scalable, and stable objective.<n>We demonstrate that our method enables sampling at unprecedented scales while preserving mode diversity, achieving state-of-the-art results on complex synthetic densities and high-dimensional molecular benchmarks.
• Score: 38.70740405520393
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Sampling from unnormalized densities using diffusion models has emerged as a powerful paradigm. However, while recent approaches that use least-squares `matching' objectives have improved scalability, they often necessitate significant trade-offs, such as restricting prior distributions or relying on unstable optimization schemes. By generalizing these methods as special forms of fixed-point iterations rooted in Nelson's relation, we develop a new method that addresses these limitations, called Bridge Matching Sampler (BMS). Our approach enables learning a stochastic transport map between arbitrary prior and target distributions with a single, scalable, and stable objective. Furthermore, we introduce a damped variant of this iteration that incorporates a regularization term to mitigate mode collapse and further stabilize training. Empirically, we demonstrate that our method enables sampling 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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