# Generative models for scalar field theories: how to deal with poor scaling?

arXiv: https://arxiv.org/abs/2301.01504 · HTML: https://mlsanity.com/paper/2301.01504/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 6 references that are in the map.
- First posted on arXiv 4 Jan 2023.

## Built on by (most cited first, 6 of 6)

- [Scaling of Stochastic Normalizing Flows in SU(3) lattice gauge theory](https://mlsanity.com/paper/2412.00200/) (2024)
- [Physics-Conditioned Diffusion Models for Lattice Gauge Theory](https://mlsanity.com/paper/2502.05504/) (2025)
- [Scaling flow-based approaches for topology sampling in SU(3) gauge theory](https://mlsanity.com/paper/2510.25704/) (2025)
- [Group-Equivariant Diffusion Models for Lattice Field Theory](https://mlsanity.com/paper/2510.26081/) (2025)
- [Detecting subtle macroscopic changes in a finite temperature classical scalar field with machine learning](https://mlsanity.com/paper/2311.12303/) (2023)
- [Accurate Sampling from Diffusion Models](https://mlsanity.com/paper/2609.29902/) (2026)

## Abstract (arXiv)

Generative models, such as the method of normalizing flows, have been suggested as alternatives to the standard algorithms for generating lattice gauge field configurations. Studies with the method of normalizing flows demonstrate the proof of principle for simple models in two dimensions. However, further studies indicate that the training cost can be, in general, very high for large lattices. The poor scaling traits of current models indicate that moderate-size networks cannot efficiently handle the inherently multi-scale aspects of the problem, especially around critical points. We explore current models with limited acceptance rates for large lattices and examine new architectures inspired by effective field theories to improve scaling traits. We also discuss alternative ways of handling poor acceptance rates for large lattices.