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.

翻译：在机器学习与生物学的交汇点上，我们揭示了扩散模型本质上是进化算法。通过将进化视为去噪过程、反向进化视为扩散过程，我们从数学上证明了扩散模型天然地执行着进化算法，自然地涵盖了选择、突变和生殖隔离等要素。基于这一等价性，我们提出了扩散进化方法：一种利用迭代去噪——最初在扩散模型背景下引入——来启发式优化参数空间中解的进化算法。与传统方法不同，扩散进化能高效识别多个最优解，并优于主流进化算法。此外，借助扩散模型中的先进概念，即潜在空间扩散和加速采样，我们提出了潜在空间扩散进化方法，该方法能在高维复杂参数空间中为进化任务寻找解，同时显著减少计算步骤。扩散与进化之间的这种对应关系不仅连接了两个不同领域，还为相互增强开辟了新途径，引发了关于开放式进化以及在扩散进化背景下潜在利用非高斯或离散扩散模型的新问题。