BranchSBM, a novel generative modeling framework, extends Schr\”odinger Bridge Matching to model branched stochastic paths and multi-path evolution from a single initial distribution to multiple outcomes.
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.