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arXiv · 2506.09007

Branched Schr\"odinger Bridge Matching

Sophia Tang·Yinuo Zhang·Alexander Tong·Pranam Chatterjee
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Abstract

Predicting the intermediate trajectories between an initial and target distribution is a central problem in generative modeling. Existing approaches, such as flow matching and Schr\"odinger bridge matching, effectively learn mappings between two distributions by modeling a single stochastic path. However, these methods are inherently limited to unimodal transitions and cannot capture branched or divergent evolution from a common origin to multiple distinct modes. To address this, we introduce Branched Schr\"odinger Bridge Matching (BranchSBM), a novel framework that learns branched Schr\"odinger bridges. BranchSBM parameterizes multiple time-dependent velocity fields and growth processes, enabling the representation of population-level divergence into multiple terminal distributions. We show that BranchSBM is not only more expressive but also essential for tasks involving multi-path surface navigation, modeling cell fate bifurcations from homogeneous progenitor states, and simulating diverging cellular responses to perturbations.

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Sophia Tang, Yinuo Zhang, Alexander Tong, Pranam Chatterjee. 2025-06-10. Branched Schr\"odinger Bridge Matching. https://arxiv.org/abs/2506.09007

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