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BM$^2$: Coupled Schr\"{o}dinger Bridge Matching
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abstract
A Schr\"{o}dinger 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 Schr\"{o}dinger 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.
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Cited by 1 Pith paper
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Incorporating Pre-trained Diffusion Models in Solving the Schr\"odinger Bridge Problem
Schrödinger Bridge models can be trained with diffusion-style mean, terminus, and flow-matching losses and initialized from pretrained diffusion models, improving image generation and unpaired translation.
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