Feedback Schrödinger Bridge Matching
This addresses the problem of inefficient training in distribution transport for researchers and practitioners by offering a more scalable and minimally supervised approach, though it is incremental as it builds on existing matching frameworks.
The paper tackles the trade-off between scalability and supervision in diffusion bridges for distribution transport by introducing Feedback Schrödinger Bridge Matching (FSBM), a semi-supervised framework that uses less than 8% of pre-aligned pairs to guide training, resulting in accelerated training and enhanced generalization.
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 many 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 (less than 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.