Feedback Schr\"odinger Bridge Matching

TL;DR

The paper introduces Feedback Schr"odinger Bridge Matching (FSBM), a semi-supervised framework that efficiently combines limited pre-aligned pairs with dynamic optimal transport to improve scalability and accuracy in distribution transport problems.

Contribution

FSBM is a novel semi-supervised matching method that incorporates minimal supervision via pre-aligned pairs into Schr"odinger bridge models, balancing scalability and optimal pairing access.

Findings

FSBM accelerates training compared to fully unsupervised methods.

FSBM improves generalization by leveraging limited paired data.

The framework effectively handles partially aligned datasets in distribution transport.

Abstract

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 Schr\"odinger 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.