Gauge Flow Models

TL;DR

Gauge Flow Models introduce a learnable Gauge Field into Flow ODEs, significantly improving generative performance and offering a new mathematical framework for flow-based generative models.

Contribution

The paper presents Gauge Flow Models, a novel class of generative models with a learnable Gauge Field, and demonstrates their superior performance over traditional flow models.

Findings

Gauge Flow Models outperform traditional flow models in experiments.

Flow Matching on Gaussian Mixture Models shows significant improvements.

Potential for broader application in generative tasks.

Abstract

This paper introduces Gauge Flow Models, a novel class of Generative Flow Models. These models incorporate a learnable Gauge Field within the Flow Ordinary Differential Equation (ODE). A comprehensive mathematical framework for these models, detailing their construction and properties, is provided. Experiments using Flow Matching on Gaussian Mixture Models demonstrate that Gauge Flow Models yields significantly better performance than traditional Flow Models of comparable or even larger size. Additionally, unpublished research indicates a potential for enhanced performance across a broader range of generative tasks.