# Gauge Flow Models

arXiv: https://arxiv.org/abs/2507.13414 · HTML: https://mlsanity.com/paper/2507.13414/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 20 references that are in the map.
- First posted on arXiv 17 Jul 2025.

## Builds on (most cited first, 7 of 7)

- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Steerable CNNs](https://mlsanity.com/paper/1612.08498/) (2016)
- [Flow Matching on General Geometries](https://mlsanity.com/paper/2302.03660/) (2023)
- [Lattice gauge equivariant convolutional neural networks](https://mlsanity.com/paper/2012.12901/) (2020)
- [Geometrical aspects of lattice gauge equivariant convolutional neural networks](https://mlsanity.com/paper/2303.11448/) (2023)

## Built on by (most cited first, 2 of 2)

- [Higher Gauge Flow Models](https://mlsanity.com/paper/2507.16334/) (2025)
- [Tensor Gauge Flow Models](https://mlsanity.com/paper/2511.17616/) (2025)

## Abstract (arXiv)

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 Additionally, unpublished research indicates a potential for enhanced performance across a broader range of generative tasks.