Diffusion Models are Evolutionary Algorithms

TL;DR

This paper reveals that diffusion models function as evolutionary algorithms and introduces Diffusion Evolution, a new method that improves solution refinement and efficiency in complex parameter spaces.

Contribution

It establishes a formal equivalence between diffusion models and evolutionary algorithms and proposes the Diffusion Evolution method for enhanced optimization.

Findings

Diffusion models inherently perform evolutionary processes.

Diffusion Evolution outperforms traditional evolutionary algorithms.

Latent Space Diffusion Evolution reduces computational steps in high-dimensional spaces.

Abstract

In a convergence of machine learning and biology, we reveal that diffusion models are evolutionary algorithms. By considering evolution as a denoising process and reversed evolution as diffusion, we mathematically demonstrate that diffusion models inherently perform evolutionary algorithms, naturally encompassing selection, mutation, and reproductive isolation. Building on this equivalence, we propose the Diffusion Evolution method: an evolutionary algorithm utilizing iterative denoising -- as originally introduced in the context of diffusion models -- to heuristically refine solutions in parameter spaces. Unlike traditional approaches, Diffusion Evolution efficiently identifies multiple optimal solutions and outperforms prominent mainstream evolutionary algorithms. Furthermore, leveraging advanced concepts from diffusion models, namely latent space diffusion and accelerated sampling, we introduce Latent Space Diffusion Evolution, which finds solutions for evolutionary tasks in high-dimensional complex parameter space while significantly reducing computational steps. This parallel between diffusion and evolution not only bridges two different fields but also opens new avenues for mutual enhancement, raising questions about open-ended evolution and potentially utilizing non-Gaussian or discrete diffusion models in the context of Diffusion Evolution.