Branched Schrödinger Bridge Matching

• URL: http://arxiv.org/abs/2506.09007v1
• Date: Tue, 10 Jun 2025 17:29:48 GMT
• Title: Branched Schrödinger Bridge Matching
• Authors: Sophia Tang, Yinuo Zhang, Alexander Tong, Pranam Chatterjee,
• Abstract summary: We introduce Branched Schr"odinger Bridge Matching (BranchSBM), a novel framework that learns branched Schr"odinger bridges.<n>BranchSBM parameterizes multiple time-dependent velocity fields and growth processes, enabling the representation of population-level divergence into terminal distributions.<n>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.
• Score: 45.105452288011726
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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 outcomes. 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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