arXiv：cs.LG· Denis Blessing, Lorenz Richter, Julius Berner, Egor Malitskiy, Gerhard Neumann·· 13 小时前
Bridge Matching Sampler：基于广义不动点扩散匹配的可扩展采样
Bridge Matching Sampler: Scalable Sampling via Generalized Fixed-Point Diffusion Matching
AI 导读
Bridge Matching Sampler（BMS）通过将最小二乘匹配方法泛化为基于 Nelson 关系的不动点迭代，实现了任意先验与目标分布之间的随机传输映射学习，同时保持可扩展性与稳定性。该方法还引入带正则项的阻尼迭代变体，以缓解模式崩塌并进一步稳定训练。在复杂合成密度和高维分子基准上，BMS 实现了当前最优结果，并支持在保持模式多样性的前提下进行大规模采样。
正文
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.
| Comments: | Preprint |
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2603.00530 [cs.LG] |
| (or arXiv:2603.00530v2 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2603.00530 arXiv-issued DOI via DataCite |
Submission history
From: Denis Blessing [view email]
[v1]
Sat, 28 Feb 2026 08:00:38 UTC (3,321 KB)
[v2]
Thu, 8 Oct 2026 21:38:41 UTC (3,363 KB)
来源：arXiv：cs.LG · arxiv.org