aiqbench analysis
This paper introduces the Bridge Matching Sampler (BMS), a novel framework that reformulates diffusion-based sampling as stable fixed-point iterations to overcome limitations in scalability and prior distribution constraints. By incorporating regularization to prevent mode collapse, the method achieves state-of-the-art performance on high-dimensional molecular benchmarks while maintaining diversity in complex synthetic densities. The work represents a significant theoretical and practical advancement in the core mechanics of generative modeling.
Bridge Matching Sampler: Scalable Sampling via Generalized Fixed-Point Diffusion Matching
arXiv:2603.00530v2 Announce Type: replace 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.
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.
Machine Learning (cs.LG)
arXiv:2603.00530 [cs.LG]
(or arXiv:2603.00530v2 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2603.00530 Focus to learn more arXiv-issued DOI via DataCite
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Full text under the publisher's open licence · 230 words
