Heuristically Adaptive Diffusion-Model Evolutionary Strategy.

Diffusion Models (DMs) and Evolutionary Algorithms (EAs) share a core generative principle: iterative refinement of random initial distributions to produce high-quality solutions. DMs degrade and restore data using Gaussian noise, enabling versatile generation, while EAs optimize numerical parameters through biologically inspired heuristics. Our research integrates these frameworks, employing deep learning-based DMs to enhance EAs across diverse domains. By iteratively refining DMs with heuristically curated databases, we generate better-adapted offspring parameters, achieving efficient convergence toward high-fitness solutions while preserving explorative diversity. DMs augment EAs with deep memory, retaining historical data and exploiting subtle correlations for refined sampling. Classifier-free guidance further enables precise control over evolutionary dynamics, targeting specific genotypical, phenotypical, or population traits. This hybrid approach transforms EAs into adaptive, memory-enhanced frameworks, offering unprecedented flexibility, and precision in evolutionary optimization, with broad implications for generative modeling and heuristic search.