# Sampling the Schwinger Model with Gauge-Equivariant Diffusion

arXiv: https://arxiv.org/abs/2606.27481 · HTML: https://mlsanity.com/paper/2606.27481/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 39 references that are in the map.
- First posted on arXiv 25 Jun 2026.

## Builds on (most cited first, 20 of 20)

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- [Gauge-equivariant flow models for sampling in lattice field theories with pseudofermions](https://mlsanity.com/paper/2207.08945/) (2022)
- [Flow-based sampling for fermionic lattice field theories](https://mlsanity.com/paper/2106.05934/) (2021)
- [Diffusion Models as Stochastic Quantization in Lattice Field Theory](https://mlsanity.com/paper/2309.17082/) (2023)
- [Flow-based sampling in the lattice Schwinger model at criticality](https://mlsanity.com/paper/2202.11712/) (2022)
- [Physics-Conditioned Diffusion Models for Lattice Gauge Theory](https://mlsanity.com/paper/2502.05504/) (2025)
- [Group-Equivariant Diffusion Models for Lattice Field Theory](https://mlsanity.com/paper/2510.26081/) (2025)
- [Diffusion model for SU(N) gauge theories](https://mlsanity.com/paper/2605.06134/) (2026)

## Abstract (arXiv)

We present a first study of a diffusion-based approach to accelerated sampling of the Nf = 2 lattice Schwinger model. Our work is inspired by recent and growing successes in developing such generative models for ensemble generation in LFT to overcome the well-known critical slowing down problem. We train a U(1)-equivariant score-based generative model to sample gauge link configurations from the marginal Schwinger model. By computing model likelihoods, we obtain unbiased estimates for observables that closely match those produced by MCMC simulations. We also demonstrate improvement over HMC as measured qualitatively by a reduction in topological freezing near critical parameters.