Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.00530 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910036515618816 |
|---|---|
| author | Blessing, Denis Richter, Lorenz Berner, Julius Malitskiy, Egor Neumann, Gerhard |
| author_facet | Blessing, Denis Richter, Lorenz Berner, Julius Malitskiy, Egor Neumann, Gerhard |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_00530 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bridge Matching Sampler: Scalable Sampling via Generalized Fixed-Point Diffusion Matching Blessing, Denis Richter, Lorenz Berner, Julius Malitskiy, Egor Neumann, Gerhard Machine Learning 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. |
| title | Bridge Matching Sampler: Scalable Sampling via Generalized Fixed-Point Diffusion Matching |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2603.00530 |