Branched Schrödinger Bridge Matching
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.
6849516c42e4f9106973f4d1
Sophia Tang
6849516c42e4f9106973f4d2
Yinuo Zhang
6849516c42e4f9106973f4d3
Alexander Tong
6849516c42e4f9106973f4d4
Pranam Chatterjee
Branched Schrödinger Bridge Matching
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.
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.
flow matching Schr\"odinger Bridge Matching Branched Schr\"odinger Bridge Matching BranchSBM time-dependent velocity fields growth processes multi-path surface navigation cell fate bifurcations cellular responses to perturbations