# Tensor Gauge Flow Models

arXiv: https://arxiv.org/abs/2511.17616 · HTML: https://mlsanity.com/paper/2511.17616/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 24 references that are in the map.
- First posted on arXiv 18 Nov 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)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [Flow Matching Guide and Code](https://mlsanity.com/paper/2412.06264/) (2024)
- [Gauge Equivariant Convolutional Networks and the Icosahedral CNN](https://mlsanity.com/paper/1902.04615/) (2019)
- [Flow Matching on General Geometries](https://mlsanity.com/paper/2302.03660/) (2023)
- [FlowMM: Generating Materials with Riemannian Flow Matching](https://mlsanity.com/paper/2406.04713/) (2024)
- [Metric Flow Matching for Smooth Interpolations on the Data Manifold](https://mlsanity.com/paper/2405.14780/) (2024)
- [Riemannian Flow Matching Policy for Robot Motion Learning](https://mlsanity.com/paper/2403.10672/) (2024)
- [Wasserstein Flow Matching: Generative modeling over families of distributions](https://mlsanity.com/paper/2411.00698/) (2024)
- [Theoretical Guarantees for High Order Trajectory Refinement in Generative Flows](https://mlsanity.com/paper/2503.09069/) (2025)
- [Towards High-Order Mean Flow Generative Models: Feasibility, Expressivity, and Provably Efficient Criteria](https://mlsanity.com/paper/2508.07102/) (2025)
- [Gauge Flow Models](https://mlsanity.com/paper/2507.13414/) (2025)

## Abstract (arXiv)

This paper introduces Tensor Gauge Flow Models, a new class of Generative Flow Models that generalize Gauge Flow Models and Higher Gauge Flow Models by incorporating higher-order Tensor Gauge Fields into the Flow Equation. This extension allows the model to encode richer geometric and gauge-theoretic structure in the data, leading to more expressive flow dynamics. Experiments on Gaussian mixture models show that Tensor Gauge Flow Models achieve improved generative performance compared to both standard and gauge flow baselines.