Branched Schr\"odinger Bridge Matching
Sophia Tang, Yinuo Zhang, Alexander Tong, Pranam Chatterjee

TL;DR
Branched Schr"odinger Bridge Matching (BranchSBM) introduces a new framework for modeling complex, multi-path stochastic processes, enabling the capture of diverging trajectories in generative modeling and biological applications.
Contribution
The paper proposes BranchSBM, a novel method that learns branched Schr"odinger bridges with multiple velocity fields, extending existing models to handle multi-modal, divergent distributions.
Findings
Enables modeling of branched, multi-path trajectories.
Improves representation of biological cell fate bifurcations.
Applicable to complex generative and biological systems.
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…
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Taxonomy
TopicsCell Image Analysis Techniques · Single-cell and spatial transcriptomics · Generative Adversarial Networks and Image Synthesis
