In a merging of machine learning and biology, we demonstrate that diffusion models function as evolutionary algorithms. By viewing evolution as a denoising process and reversed evolution as diffusion, we mathematically show that diffusion models inherently implement evolutionary algorithms, naturally incorporating selection, mutation, and reproductive isolation. Based on this connection, we introduce the Diffusion Evolution method, which is an evolutionary algorithm that uses iterative denoisingâ€”originally presented in the context of diffusion modelsâ€”to heuristically refine solutions in parameter spaces. Unlike traditional methods, Diffusion Evolution efficiently identifies multiple optimal solutions and surpasses leading mainstream evolutionary algorithms. Additionally, by utilizing advanced concepts from diffusion models, such as latent space diffusion and accelerated sampling, we present Latent Space Diffusion Evolution, which solves evolutionary tasks in high-dimensional, complex parameter spaces while significantly minimizing computational steps. This connection between diffusion and evolution not only links two distinct fields but also paves the way for mutual advancements, raising inquiries about open-ended evolution and the potential use of non-Gaussian or discrete diffusion models in the context of Diffusion Evolution.

Iâ€™m not a fan of the â€śX are Yâ€ť title meme. If Y truly generalizes X, thatâ€™s fantastic, but often X is only Y in a vague way, if you really stretch the meaning.

Since diffusion models are executing annealed Langevin diffusion in the backward direction, isnâ€™t the connection clear, considering the established links between annealed MCMC algorithms, simultaneous annealing, and evolutionary algorithms? Am I overlooking something?

I was just working on something like this, glad someone can lend a hand!

Makes sense. Because of constructal law, there is a ton of shared methods used by very efficient systems, from very distant domains.

Thatâ€™s true, but as you mentioned, itâ€™s acceptable if itâ€™s genuinely accurate. A quick read suggests it makes sense in this case since the paperâ€™s premise is that they can mathematically model diffusion as evolutionary algorithms.

Personally, I prefer a title that clearly conveys their main ideas rather than something like â€śMathematically modeling diffusion models in latent space as evolutionary algorithms with exact solutions and a new means of efficient construction.â€ť Iâ€™d get that information from the abstract anyway. I just need the title to indicate relevance and be easy to remember so I can locate it later.