Likelihood Training of Schrödinger Bridge using Forward-Backward SDEs Theory
This work addresses a foundational gap in generative modeling by enabling principled likelihood training for SB models, potentially benefiting researchers and practitioners in machine learning, though it is incremental as it builds on existing SB and SGM frameworks.
The authors tackled the problem of connecting Schrödinger Bridge (SB) models to likelihood-based training in deep generative modeling by developing a computational framework using Forward-Backward Stochastic Differential Equations Theory, which achieved comparable results in generating realistic images on MNIST, CelebA, and CIFAR10 datasets.
Schrödinger Bridge (SB) is an entropy-regularized optimal transport problem that has received increasing attention in deep generative modeling for its mathematical flexibility compared to the Scored-based Generative Model (SGM). However, it remains unclear whether the optimization principle of SB relates to the modern training of deep generative models, which often rely on constructing log-likelihood objectives.This raises questions on the suitability of SB models as a principled alternative for generative applications. In this work, we present a novel computational framework for likelihood training of SB models grounded on Forward-Backward Stochastic Differential Equations Theory - a mathematical methodology appeared in stochastic optimal control that transforms the optimality condition of SB into a set of SDEs. Crucially, these SDEs can be used to construct the likelihood objectives for SB that, surprisingly, generalizes the ones for SGM as special cases. This leads to a new optimization principle that inherits the same SB optimality yet without losing applications of modern generative training techniques, and we show that the resulting training algorithm achieves comparable results on generating realistic images on MNIST, CelebA, and CIFAR10. Our code is available at https://github.com/ghliu/SB-FBSDE.