2023/10/03 by Guan-Horng Liu, Yaron Lipman, Liu, Guan-Horng +9 · 2 citations
Computer Science · #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and Algorithms #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2310.02233
openalex publication_date 2023/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Modern distribution matching algorithms for training diffusion or flow models directly prescribe the time evolution of the marginal distributions between two boundary distributions. In this work, we consider a generalized distribution matching setup, where these marginals are only implicitly described as a solution to some task-specific objective function. The problem setup, known as the Generalized Schrödinger Bridge (GSB), appears prevalently in many scientific areas both within and without machine learning. We propose Generalized Schrödinger Bridge Matching (GSBM), a new matching algorithm inspired by recent advances, generalizing them beyond kinetic energy minimization and to account for task-specific state costs. We show that such a generalization can be cast as solving conditional stochastic optimal control, for which efficient variational approximations can be used, and further debiased with the aid of path integral theory. Compared to prior methods for solving GSB problems, our GSBM algorithm better preserves a feasible transport map between the boundary distributions throughout training, thereby enabling stable convergence and significantly improved scalability. We empirically validate our claims on an extensive suite of experimental setups, including crowd navigation, opinion depolarization, LiDAR manifolds, and image domain transfer. Our work brings new algorithmic opportunities for training diffusion models enhanced with task-specific optimality structures. Code available at https://github.com/facebookresearch/generalized-schrodinger-bridge-matching