Higher Gauge Flow Models

TL;DR

This paper presents Higher Gauge Flow Models, an advanced generative modeling approach that incorporates higher algebraic structures to improve performance, extending traditional gauge flow models with higher symmetries.

Contribution

It introduces Higher Gauge Flow Models that integrate L-infinity algebras and higher symmetries into generative flow frameworks, advancing beyond previous gauge flow models.

Findings

Significant performance improvements on Gaussian Mixture Model datasets.

Effective incorporation of higher geometry and symmetries into flow models.

Abstract

This paper introduces Higher Gauge Flow Models, a novel class of Generative Flow Models. Building upon ordinary Gauge Flow Models (arXiv:2507.13414), these Higher Gauge Flow Models leverage an L$_{\infty}$-algebra, effectively extending the Lie Algebra. This expansion allows for the integration of the higher geometry and higher symmetries associated with higher groups into the framework of Generative Flow Models. Experimental evaluation on a Gaussian Mixture Model dataset revealed substantial performance improvements compared to traditional Flow Models.