# Toward Scalable Normalizing Flows for the Hubbard Model

arXiv: https://arxiv.org/abs/2601.18273 · HTML: https://mlsanity.com/paper/2601.18273/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 35 references that are in the map.
- First posted on arXiv 26 Jan 2026.

## Builds on (most cited first, 17 of 17)

- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Pixel Recurrent Neural Networks](https://mlsanity.com/paper/1601.06759/) (2016)
- [Symmetry-adapted generation of 3d point sets for the targeted discovery of molecules](https://mlsanity.com/paper/1906.00957/) (2019)
- [Stochastic Normalizing Flows](https://mlsanity.com/paper/2002.06707/) (2020)
- [Flow-based generative models for Markov chain Monte Carlo in lattice field theory](https://mlsanity.com/paper/1904.12072/) (2019)
- [Solving Statistical Mechanics Using Variational Autoregressive Networks](https://mlsanity.com/paper/1809.10606/) (2018)
- [Inverse design of 3d molecular structures with conditional generative neural networks](https://mlsanity.com/paper/2109.04824/) (2021)
- [Stochastic normalizing flows as non-equilibrium transformations](https://mlsanity.com/paper/2201.08862/) (2022)
- [Advances in machine-learning-based sampling motivated by lattice quantum chromodynamics](https://mlsanity.com/paper/2309.01156/) (2023)
- [Flow-Based Sampling for Entanglement Entropy and the Machine Learning of Defects](https://mlsanity.com/paper/2410.14466/) (2024)
- [Sampling the lattice Nambu-Goto string using Continuous Normalizing Flows](https://mlsanity.com/paper/2307.01107/) (2023)
- [Scaling of Stochastic Normalizing Flows in SU(3) lattice gauge theory](https://mlsanity.com/paper/2412.00200/) (2024)
- [Numerical determination of the width and shape of the effective string using Stochastic Normalizing Flows](https://mlsanity.com/paper/2409.15937/) (2024)
- [Scaling flow-based approaches for topology sampling in SU(3) gauge theory](https://mlsanity.com/paper/2510.25704/) (2025)
- [SESaMo: Symmetry-Enforcing Stochastic Modulation for Normalizing Flows](https://mlsanity.com/paper/2505.19619/) (2025)
- [Simulating Correlated Electrons with Symmetry-Enforced Normalizing Flows](https://mlsanity.com/paper/2506.17015/) (2025)

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

- [A scalable flow-based approach to mitigate topological freezing](https://mlsanity.com/paper/2601.20708/) (2026)
- [Tackling the Sign Problem in the Doped Hubbard Model with Normalizing Flows](https://mlsanity.com/paper/2603.18205/) (2026)

## Abstract (arXiv)

Normalizing flows have recently demonstrated the ability to learn the Boltzmann distribution of the Hubbard model, opening new avenues for generative modeling in condensed matter physics. In this work, we investigate the steps required to extend such simulations to larger lattice sizes and lower temperatures, with a focus on enhancing stability and efficiency. Additionally, we present the scaling behavior of stochastic normalizing flows and non-equilibrium Markov chain Monte Carlo methods for this fermionic system.