Diffusion Models represent a significant advancement in generative modeling, employing a dual-phase process that first degrades domain-specific information via Gaussian noise and restores it through a trainable model. This framework enables pure noise-to-data generation and modular reconstruction of, images or videos. Concurrently, evolutionary algorithms employ optimization methods inspired by biological principles to refine sets of numerical parameters encoding potential solutions to rugged objective functions. Our research reveals a fundamental connection between diffusion models and evolutionary algorithms through their shared underlying generative mechanisms: both methods generate high-quality samples via iterative refinement on random initial distributions. By employing deep learning-based diffusion models as generative models across diverse evolutionary tasks and iteratively refining diffusion models with heuristically acquired databases, we can iteratively sample potentially better-adapted offspring parameters, integrating them into successive generations of the diffusion model. This approach achieves efficient convergence toward high-fitness parameters while maintaining explorative diversity. Diffusion models introduce enhanced memory capabilities into evolutionary algorithms, retaining historical information across generations and leveraging subtle data correlations to generate refined samples. We elevate evolutionary algorithms from procedures with shallow heuristics to frameworks with deep memory. By deploying classifier-free guidance for conditional sampling at the parameter level, we achieve precise control over evolutionary search dynamics to further specific genotypical, phenotypical, or population-wide traits. Our framework marks a major heuristic and algorithmic transition, offering increased flexibility, precision, and control in evolutionary optimization processes.

翻译：扩散模型代表了生成建模领域的一项重大进展，它采用双阶段过程：首先通过高斯噪声降解特定领域的信息，然后通过可训练模型恢复信息。该框架实现了从纯噪声到数据的生成，以及对图像或视频的模块化重建。与此同时，进化算法采用受生物学原理启发的优化方法，对编码崎岖目标函数潜在解的一组数值参数进行精炼。我们的研究揭示了扩散模型与进化算法之间通过其共享的底层生成机制存在根本联系：两种方法都是通过对随机初始分布进行迭代精炼来生成高质量样本。通过将基于深度学习的扩散模型用作跨多种进化任务的生成模型，并利用启发式获取的数据库迭代精炼扩散模型，我们能够迭代采样潜在适应性更强的子代参数，并将其整合到扩散模型的连续世代中。这种方法在保持探索多样性的同时，实现了向高适应度参数的高效收敛。扩散模型为进化算法引入了增强的记忆能力，能够跨世代保留历史信息，并利用细微的数据相关性生成精炼样本。我们将进化算法从浅层启发式过程提升为具有深度记忆的框架。通过在参数层面部署无分类器引导进行条件采样，我们实现了对进化搜索动态的精确控制，以进一步优化特定的基因型、表型或群体层面的特征。我们的框架标志着一个重大的启发式与算法转变，为进化优化过程提供了更高的灵活性、精确性和可控性。