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叉中，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、将反向进化视为扩散过程，我们从数学上证明扩散模型天然具备执行进化算法的能力，并自然涵盖了选择、变异和生殖隔离等关键机制。基于这种等价性，我们提出了"扩散进化"方法：这是一种利用迭代去噪（该思想最初源自扩散模型领域）在参数空间中启发式优化解的进化算法。与传统方法不同，扩散进化能高效识别多个最优解，并显著优于主流进化算法。进一步地，通过借鉴扩散模型的先进概念（即潜空间扩散与加速采样），我们引入了"潜空间扩散进化"方法，它能在高维复杂参数空间中找到进化任务的解，同时大幅减少计算步数。这种扩散与进化的双向映射不仅架起了两大学科之间的桥梁，更为相互促进开辟了新途径——它引发了关于开放性进化的思考，并可能推动非高斯或离散扩散模型在扩散进化场景中的应用。