BM$^2$: Coupled Schrödinger Bridge Matching
This work addresses a specific problem in generative modeling and optimal transport for researchers in machine learning, presenting an incremental improvement with a new method for a known bottleneck.
The paper tackles the problem of learning Schrödinger bridges between two target distributions using available samples and a tractable reference diffusion process, introducing Coupled Bridge Matching (BM²) as a simple non-iterative neural network approach, with numerical experiments demonstrating its effectiveness.
A Schrödinger bridge establishes a dynamic transport map between two target distributions via a reference process, simultaneously solving an associated entropic optimal transport problem. We consider the setting where samples from the target distributions are available, and the reference diffusion process admits tractable dynamics. We thus introduce Coupled Bridge Matching (BM$^2$), a simple non-iterative approach for learning Schrödinger bridges with neural networks. A preliminary theoretical analysis of the convergence properties of BM$^2$ is carried out, supported by numerical experiments that demonstrate the effectiveness of our proposal.