Branched Schrödinger Bridge Matching
This addresses the need for modeling branched or divergent evolution in generative tasks, such as in biology for cell fate studies, representing a novel extension beyond incremental improvements.
The paper tackles the problem of predicting intermediate trajectories between initial and target distributions in generative modeling, which is limited by existing methods to unimodal transitions, and introduces Branched Schrödinger Bridge Matching (BranchSBM) to enable branched evolution from a common origin to multiple distinct outcomes, showing its expressiveness and essentiality for tasks like multi-path navigation and cell fate bifurcations.
Predicting the intermediate trajectories between an initial and target distribution is a central problem in generative modeling. Existing approaches, such as flow matching and Schrödinger 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 Schrödinger Bridge Matching (BranchSBM), a novel framework that learns branched Schrödinger 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.