# Diffusion Models are Evolutionary Algorithms

arXiv: https://arxiv.org/abs/2410.02543 · HTML: https://mlsanity.com/paper/2410.02543/

## Key facts

- Cited by 17 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 65 references that are in the map.
- First posted on arXiv 3 Oct 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)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (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)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Evolution Strategies as a Scalable Alternative to Reinforcement Learning](https://mlsanity.com/paper/1703.03864/) (2017)
- [Illuminating search spaces by mapping elites](https://mlsanity.com/paper/1504.04909/) (2015)
- [The CMA Evolution Strategy: A Tutorial](https://mlsanity.com/paper/1604.00772/) (2016)
- [Cold Diffusion: Inverting Arbitrary Image Transforms Without Noise](https://mlsanity.com/paper/2208.09392/) (2022)
- [Residual Flows for Invertible Generative Modeling](https://mlsanity.com/paper/1906.02735/) (2019)
- [Spontaneous Symmetry Breaking in Generative Diffusion Models](https://mlsanity.com/paper/2305.19693/) (2023)
- [Diffusion Models for Black-Box Optimization](https://mlsanity.com/paper/2306.07180/) (2023)
- [Neural Network Diffusion](https://mlsanity.com/paper/2402.13144/) (2024)
- [Technological Approach to Mind Everywhere (TAME): an experimentally-grounded framework for understanding diverse bodies and minds](https://mlsanity.com/paper/2201.10346/) (2021)
- [Towards a Theory of Evolution as Multilevel Learning](https://mlsanity.com/paper/2110.14602/) (2021)
- [EmoDM: A Diffusion Model for Evolutionary Multi-objective Optimization](https://mlsanity.com/paper/2401.15931/) (2024)

## Built on by (most cited first, 17 of 17)

- [Neural cellular automata: applications to biology and beyond classical AI](https://mlsanity.com/paper/2509.11131/) (2025)
- [Towards Deploying VLA without Fine-Tuning: Plug-and-Play Inference-Time VLA Policy Steering via Embodied Evolutionary Diffusion](https://mlsanity.com/paper/2511.14178/) (2025)
- [Heuristically Adaptive Diffusion-Model Evolutionary Strategy](https://mlsanity.com/paper/2411.13420/) (2024)
- [Stein Variational Evolution Strategies](https://mlsanity.com/paper/2410.10390/) (2024)
- [Diffusion-based learning framework for Constrained Nonconvex Optimization with Weighted Bootstrapped Refinement](https://mlsanity.com/paper/2502.10330/) (2025)
- [Evolution Meets Diffusion: Efficient Neural Architecture Generation](https://mlsanity.com/paper/2504.17827/) (2025)
- [DoublyAware: Dual Planning and Policy Awareness for Temporal Difference Learning in Humanoid Locomotion](https://mlsanity.com/paper/2506.12095/) (2025)
- [A Unification of Discrete, Gaussian, and Simplicial Diffusion](https://mlsanity.com/paper/2512.15923/) (2025)
- [Remapping and navigation of an embedding space via error minimization: a fundamental organizational principle of cognition in natural and artificial systems](https://mlsanity.com/paper/2601.14096/) (2026)
- [Regret Analysis of Guided Diffusion for Black-Box Optimization over Structured Inputs](https://mlsanity.com/paper/2605.10385/) (2026)
- [Diverse and Adaptable Arm Coordination for Octopus-Crawling via Diffusion-Based Uncertainty-Aware Optimization](https://mlsanity.com/paper/2609.21138/) (2026)
- [Weak Supervision Dynamic KL-Weighted Diffusion Models Guided by Large Language Models](https://mlsanity.com/paper/2502.00826/) (2025)
- [Model Tensor Planning](https://mlsanity.com/paper/2505.01059/) (2025)
- [Evolutionary Computation as Natural Generative AI](https://mlsanity.com/paper/2510.08590/) (2025)
- [Diffusion Crossover: Defining Evolutionary Recombination in Diffusion Models via Noise Sequence Interpolation](https://mlsanity.com/paper/2604.14790/) (2026)
- [Bridging Spherical Black-Box Optimizers](https://mlsanity.com/paper/2606.25761/) (2026)
- [DiffGA: Steering Frozen Diffusion Models for Materials Design via Evolutionary Search](https://mlsanity.com/paper/2610.14999/) (2026)

## Abstract (arXiv)

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.