Branched Schrödinger Bridge Matching
Authors: name: Sophia Tang, name: Yinuo Zhang, name: Alexander Tong, name: Pranam Chatterjee

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.