Bridge Matching Sampler: Scalable Sampling via Generalized Fixed-Point Diffusion Matching
This addresses scalability and stability issues in diffusion-based sampling for applications like molecular modeling, though it appears incremental as it builds on existing matching objectives.
The paper tackled the problem of sampling from unnormalized densities using diffusion models by developing the Bridge Matching Sampler (BMS), which generalizes fixed-point iterations to learn stochastic transport maps between arbitrary distributions, achieving state-of-the-art results on complex synthetic and high-dimensional molecular benchmarks.
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.