Feedback Schrödinger Bridge Matching
Panagiotis Theodoropoulos Nikolaos Komianos Vincent Pacelli Guan-Horng Liu Evangelos Theodorou
Recent advancements in diffusion bridges for distribution transport problems have heavily relied on matching frameworks, yet existing methods often face a trade-off between scalability and access to optimal pairings during training. 
Fully unsupervised methods make minimal assumptions but incur high computational costs, limiting their practicality. On the other hand, imposing full supervision of the matching process with optimal pairings improves scalability, however, it can be infeasible in most applications.
To strike a balance between scalability and minimal supervision, we introduce Feedback Schrödinger Bridge Matching (FSBM), a novel semi-supervised matching framework that incorporates a small portion ($<8$% of the entire dataset) of pre-aligned pairs as state feedback to guide the transport map of non-coupled samples, thereby significantly improving efficiency. This is achieved by formulating a static Entropic Optimal Transport (EOT) problem with an additional term capturing the semi-supervised guidance. The generalized EOT objective is then recast into a dynamic formulation to leverage the scalability of matching frameworks. Extensive experiments demonstrate that FSBM accelerates training and enhances generalization by leveraging coupled pairs' guidance, opening new avenues for training matching frameworks with partially aligned datasets.
Diffusion models, Schrödinger bridge, Distribution matching, Semi-Supervised Learning
We introduce Feedback Schrödinger Bridge Matching, a novel semi-supervised framework that uses pre-aligned pairs to guide the matching of non-coupled samples.