BM$^2$: Coupled Schrödinger Bridge Matching
Abstract: 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 \emph{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.
Submission Length: Regular submission (no more than 12 pages of main content)
Assigned Action Editor: ~Alain_Durmus1
Submission Number: 3342
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