# Equivariant flow-based sampling for lattice gauge theory

arXiv: https://arxiv.org/abs/2003.06413 · HTML: https://mlsanity.com/paper/2003.06413/

## Key facts

- Cited by 103 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Mar 2020.

## Built on by (most cited first, 30 of 103)

- [SE(3)-Stochastic Flow Matching for Protein Backbone Generation](https://mlsanity.com/paper/2310.02391/) (2023)
- [Equivariant flow matching](https://mlsanity.com/paper/2306.15030/) (2023)
- [Predicting Physics in Mesh-reduced Space with Temporal Attention](https://mlsanity.com/paper/2201.09113/) (2022)
- [Spontaneous Symmetry Breaking in Generative Diffusion Models](https://mlsanity.com/paper/2305.19693/) (2023)
- [A Living Review of Machine Learning for Particle Physics](https://mlsanity.com/paper/2102.02770/) (2021)
- [Swallowing the Bitter Pill: Simplified Scalable Conformer Generation](https://mlsanity.com/paper/2311.17932/) (2023)
- [Learning Lattice Quantum Field Theories with Equivariant Continuous Flows](https://mlsanity.com/paper/2207.00283/) (2022)
- [EDGI: Equivariant Diffusion for Planning with Embodied Agents](https://mlsanity.com/paper/2303.12410/) (2023)
- [Machine-learning hidden symmetries](https://mlsanity.com/paper/2109.09721/) (2021)
- [Symmetry-via-Duality: Invariant Neural Network Densities from Parameter-Space Correlators](https://mlsanity.com/paper/2106.00694/) (2021)
- [Scalable Discrete Diffusion Samplers: Combinatorial Optimization and Statistical Physics](https://mlsanity.com/paper/2502.08696/) (2025)
- [Neural Importance Sampling for Rapid and Reliable Gravitational-Wave Inference](https://mlsanity.com/paper/2210.05686/) (2022)
- [Aspects of scaling and scalability for flow-based sampling of lattice QCD](https://mlsanity.com/paper/2211.07541/) (2022)
- [Sampling with flows, diffusion and autoregressive neural networks: A spin-glass perspective](https://mlsanity.com/paper/2308.14085/) (2023)
- [Stochastic normalizing flows as non-equilibrium transformations](https://mlsanity.com/paper/2201.08862/) (2022)
- [Scaling Up Machine Learning For Quantum Field Theory with Equivariant Continuous Flows](https://mlsanity.com/paper/2110.02673/) (2021)
- [Diffusion Models as Stochastic Quantization in Lattice Field Theory](https://mlsanity.com/paper/2309.17082/) (2023)
- [Symmetry Group Equivariant Architectures for Physics](https://mlsanity.com/paper/2203.06153/) (2022)
- [Gradients should stay on Path: Better Estimators of the Reverse- and Forward KL Divergence for Normalizing Flows](https://mlsanity.com/paper/2207.08219/) (2022)
- [Advances in machine-learning-based sampling motivated by lattice quantum chromodynamics](https://mlsanity.com/paper/2309.01156/) (2023)
- [Deep Learning Symmetries and Their Lie Groups, Algebras, and Subalgebras from First Principles](https://mlsanity.com/paper/2301.05638/) (2023)
- [Tilt Matching for Scalable Sampling and Fine-Tuning](https://mlsanity.com/paper/2512.21829/) (2025)
- [Topological Obstructions to Autoencoding](https://mlsanity.com/paper/2102.08380/) (2021)
- [Dynamical Measure Transport and Neural PDE Solvers for Sampling](https://mlsanity.com/paper/2407.07873/) (2024)
- [Gauge Invariant and Anyonic Symmetric Transformer and RNN Quantum States for Quantum Lattice Models](https://mlsanity.com/paper/2101.07243/) (2021)
- [Generalization capabilities of translationally equivariant neural networks](https://mlsanity.com/paper/2103.14686/) (2021)
- [Quantum field-theoretic machine learning](https://mlsanity.com/paper/2102.09449/) (2021)
- [Ab-initio study of interacting fermions at finite temperature with neural canonical transformation](https://mlsanity.com/paper/2105.08644/) (2021)
- [Renormalizing Diffusion Models](https://mlsanity.com/paper/2308.12355/) (2023)
- [Applications of Machine Learning to Lattice Quantum Field Theory](https://mlsanity.com/paper/2202.05838/) (2022)

## Abstract (arXiv)

We define a class of machine-learned flow-based sampling algorithms for lattice gauge theories that are gauge-invariant by construction. We demonstrate the application of this framework to U(1) gauge theory in two spacetime dimensions, and find that near critical points in parameter space the approach is orders of magnitude more efficient at sampling topological quantities than more traditional sampling procedures such as Hybrid Monte Carlo and Heat Bath.