# Non-equilibrium active noise enhances generative memory in diffusion models

arXiv: https://arxiv.org/abs/2411.07233 · HTML: https://mlsanity.com/paper/2411.07233/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 19 of its 42 references that are in the map.
- First posted on arXiv 11 Nov 2024.

## Placed in

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

## Builds on (most cited first, 19 of 19)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Zero-Shot Text-to-Image Generation](https://mlsanity.com/paper/2102.12092/) (2021)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)
- [Score-Based Generative Modeling with Critically-Damped Langevin Diffusion](https://mlsanity.com/paper/2112.07068/) (2021)
- [Gotta Go Fast When Generating Data with Score-Based Models](https://mlsanity.com/paper/2105.14080/) (2021)
- [Dynamical Regimes of Diffusion Models](https://mlsanity.com/paper/2402.18491/) (2024)
- [Wavelet Diffusion Models are fast and scalable Image Generators](https://mlsanity.com/paper/2211.16152/) (2022)
- [Theoretical guarantees for sampling and inference in generative models with latent diffusions](https://mlsanity.com/paper/1903.01608/) (2019)
- [A Phase Transition in Diffusion Models Reveals the Hierarchical Nature of Data](https://mlsanity.com/paper/2402.16991/) (2024)
- [Discovering Interpretable Directions in the Semantic Latent Space of Diffusion Models](https://mlsanity.com/paper/2303.11073/) (2023)
- [Speed Is All You Need: On-Device Acceleration of Large Diffusion Models via GPU-Aware Optimizations](https://mlsanity.com/paper/2304.11267/) (2023)
- [Non-normal Recurrent Neural Network (nnRNN): learning long time dependencies while improving expressivity with transient dynamics](https://mlsanity.com/paper/1905.12080/) (2019)
- [Exploring the Optimal Choice for Generative Processes in Diffusion Models: Ordinary vs Stochastic Differential Equations](https://mlsanity.com/paper/2306.02063/) (2023)
- [Turbulence Scaling from Deep Learning Diffusion Generative Models](https://mlsanity.com/paper/2311.06112/) (2023)

## Built on by (most cited first, 1 of 1)

- [An effective potential for generative modelling with active matter](https://mlsanity.com/paper/2508.08146/) (2025)

## Abstract (arXiv)

Generative diffusion models have emerged as powerful tools for sampling high-dimensional distributions, yet they typically rely on white gaussian noise and noise schedules to destroy and reconstruct information. Here, we demonstrate that driving the generative process out of equilibrium using active, temporally correlated noise sources fundamentally alters the information thermodynamics of the system. We show that coupling the data to an active non-Markovian bath creates a `memory effect' where high-level semantic information (such as class identity or molecular metastability) is stored in the temporal correlations of auxiliary degrees of freedom. Using Fisher information analysis, we prove that this active mechanism significantly retards the rate of information decay compared to passive Brownian motion. Crucially, this memory effect facilitates an earlier and more robust symmetry breaking (speciation) during the reverse generative process, allowing the system to resolve multi-scale structures, reminiscent of metastable states in molecular configurations that are washed out in the typical noising processes. Our results suggest that non-equilibrium protocols, inspired by active matter physics, offer a thermodynamically distinct and potentially advantageous pathway for recovering high-dimensional energy landscapes using generative diffusion.