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

Understand

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.