Generalized Schrödinger Bridge Matching
This work addresses distribution matching in diffusion models with task-specific optimality, offering improved algorithmic opportunities for applications in machine learning and scientific domains, though it appears incremental as it generalizes existing methods.
The authors tackled the Generalized Schrödinger Bridge (GSB) problem, which involves matching distributions with task-specific objectives, by proposing Generalized Schrödinger Bridge Matching (GSBM), a new algorithm that improves stability and scalability compared to prior methods, as validated on tasks like crowd navigation and image domain transfer.
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