# Information Spreading in Diffusion Models from Effective Field Theory

arXiv: https://arxiv.org/abs/2608.14308 · HTML: https://mlsanity.com/paper/2608.14308/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 16 of its 24 references that are in the map.
- First posted on arXiv 14 Aug 2026.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 16 of 16)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [Dynamical Regimes of Diffusion Models](https://mlsanity.com/paper/2402.18491/) (2024)
- [An analytic theory of creativity in convolutional diffusion models](https://mlsanity.com/paper/2412.20292/) (2024)
- [Spontaneous Symmetry Breaking in Generative Diffusion Models](https://mlsanity.com/paper/2305.19693/) (2023)
- [Information-Theoretic Diffusion](https://mlsanity.com/paper/2302.03792/) (2023)
- [Diffusion Models for Non-autoregressive Text Generation: A Survey](https://mlsanity.com/paper/2303.06574/) (2023)
- [Locality in Image Diffusion Models Emerges from Data Statistics](https://mlsanity.com/paper/2509.09672/) (2025)
- [How Out-of-Equilibrium Phase Transitions can Seed Pattern Formation in Trained Diffusion Models](https://mlsanity.com/paper/2603.20092/) (2026)

## Abstract (arXiv)

We study score-matching diffusion models with a convolutional architecture. We argue that the inductive bias of locality means that the machinery of effective field theory from physics can be usefully applied to describe the denoising dynamics. We apply this formalism first to a simple toy example which permits an analytical description, and thereafter to MNIST, and show that in both cases, the mutual information between two points grows in a manner predicted by a simple effective field theory of Brownian motion.