# Higher Gauge Flow Models

arXiv: https://arxiv.org/abs/2507.16334 · HTML: https://mlsanity.com/paper/2507.16334/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 45 references that are in the map.
- First posted on arXiv 22 Jul 2025.

## Builds on (most cited first, 14 of 14)

- [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)
- [Flow Matching on General Geometries](https://mlsanity.com/paper/2302.03660/) (2023)
- [Backprop as Functor: A compositional perspective on supervised learning](https://mlsanity.com/paper/1711.10455/) (2017)
- [Categorical Foundations of Gradient-Based Learning](https://mlsanity.com/paper/2103.01931/) (2021)
- [Category Theory in Machine Learning](https://mlsanity.com/paper/2106.07032/) (2021)
- [Position: Categorical Deep Learning is an Algebraic Theory of All Architectures](https://mlsanity.com/paper/2402.15332/) (2024)
- [Lenses and Learners](https://mlsanity.com/paper/1903.03671/) (2019)
- [Fundamental Components of Deep Learning: A category-theoretic approach](https://mlsanity.com/paper/2403.13001/) (2024)
- [Homotopy Theoretic and Categorical Models of Neural Information Networks](https://mlsanity.com/paper/2006.15136/) (2020)
- [Dynamic Operads, Dynamic Categories: From Deep Learning to Prediction Markets](https://mlsanity.com/paper/2205.03906/) (2022)
- [Towards a Categorical Foundation of Deep Learning: A Survey](https://mlsanity.com/paper/2410.05353/) (2024)
- [Gauge Flow Models](https://mlsanity.com/paper/2507.13414/) (2025)

## Abstract (arXiv)

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∞-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.