Extended Flow Matching: a Method of Conditional Generation with Generalized Continuity Equation

TL;DR

This paper introduces Extended Flow Matching (EFM), a novel conditional generative modeling approach that incorporates an explicit inductive bias via a matrix field, improving control over condition-dependent distribution changes.

Contribution

EFM extends flow matching by learning a matrix field to explicitly model how distributions change with conditions, enabling better inductive bias in conditional generation.

Findings

EFM demonstrates competitive performance in conditional generation tasks.

Incorporating the matrix field improves control over distribution sensitivity.

Experimental results validate the effectiveness of EFM compared to existing methods.

Abstract

The task of conditional generation is one of the most important applications of generative models, and numerous methods have been developed to date based on the celebrated flow-based models. However, many flow-based models in use today are not built to allow one to introduce an explicit inductive bias to how the conditional distribution to be generated changes with respect to conditions. This can result in unexpected behavior in the task of style transfer, for example. In this research, we introduce extended flow matching (EFM), a direct extension of flow matching that learns a "matrix field" corresponding to the continuous map from the space of conditions to the space of distributions. We show that we can introduce inductive bias to the conditional generation through the matrix field and demonstrate this fact with MMOT-EFM, a version of EFM that aims to minimize the Dirichlet energy or the sensitivity of the distribution with respect to conditions. We will present our theory along with experimental results that support the competitiveness of EFM in conditional generation.