Branched Schr""odinger Bridge Matching

2025-06-10

AI Summary

Existing generative modeling approaches—such as flow matching and Schrödinger bridges—rely on a single-path assumption, limiting their ability to capture dynamic branching processes where a shared initial distribution evolves toward multiple heterogeneous terminal states. To address this, we propose the Branching Schrödinger Bridge (BSB) framework, the first method enabling joint modeling of multiple terminal distributions. BSB introduces a time-varying multi-head vector field and a growth-process parameterization to explicitly learn population-level divergence trajectories. Grounded in optimal transport theory, it incorporates joint terminal constraints into the variational optimization objective. Experiments demonstrate that BSB significantly outperforms baseline methods on cell fate differentiation simulation and multi-path surface navigation tasks, accurately reproducing complex bifurcating dynamics—including double-bifurcation patterns. By unifying branching structure learning with stochastic transport, BSB establishes a new paradigm for modeling multi-outcome evolutionary processes.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Planning, Routing, and Scheduling: Planning/Scheduling and Learning
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational 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 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.

Problem

• Modeling branched evolution from single origin to multiple outcomes
• Capturing divergent trajectories between initial and target distributions
• Enabling multi-path navigation and cell fate bifurcation modeling

Innovation

• Introduces Branched Schru00f6dinger Bridge Matching
• Parameterizes multiple velocity fields
• Enables population-level divergence modeling