[2603.00530] Bridge Matching Sampler: Scalable Sampling via Generalized Fixed-Point Diffusion Matching

Computer Science > Machine Learning arXiv:2603.00530 (cs) [Submitted on 28 Feb 2026] Title:Bridge Matching Sampler: Scalable Sampling via Generalized Fixed-Point Diffusion Matching Authors:Denis Blessing, Lorenz Richter, Julius Berner, Egor Malitskiy, Gerhard Neumann View a PDF of the paper titled Bridge Matching Sampler: Scalable Sampling via Generalized Fixed-Point Diffusion Matching, by Denis Blessing and 4 other authors View PDF HTML (experimental) 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 ...