Benedikt Hartl

Diffusion Models (DMs) represent a significant advancement in generative modeling, employing a two-stage process that first degrades domain-specific information via Gaussian noise, then restores it through a trainable model. This framework enables pure noise-to-data generation as well as modular reconstruction of, e.g., images or videos. Evolutionary Algorithms (EAs) employ biologically inspired methods such as genotypic recombination and mutation operations of selected high-fitness candidate solutions to heuristically refine sets of numerical parameters that encode potential solutions to rugged objective functions. Our research reveals a fundamental connection between DMs and EAs through their shared underlying generative mechanisms: both methods generate high-quality samples via structured iterative refinement on random initial distributions. This conceptual equivalence has led to the development of the Diffusion Evolution method [1], a competitive model-free evolutionary strategy that integrates denoising principles to explore complex parameter spaces. Our Hierarchical Adaptive Diffusion Evolution Strategy (HADES) [2] builds on these insights by employing deep learning-based DMs to sample high-quality offspring candidates in evolutionary optimization tasks. HADES enhances the evolutionary optimization process with deep memory by iteratively retraining a DM on heuristically acquired parameter and fitness data across generations. This enables the generative evolutionary process to utilize subtle correlations in the genetic parameters and efficiently guide the evolutionary population toward high-fitness regions in the parameter space. In that way, we leverage EAs from procedures with shallow heuristics to sophisticated frameworks with deep memory while maintaining explorative diversity. Moreover, classifier-free guidance techniques allow for conditional sampling of offspring parameters, enabling precise control over the evolutionary search dynamics by simply conditioning the DM's generative process - as opposed to reward-shaping techniques - on target genotypical, phenotypical, or population-wide traits. This Conditional Diffusion Evolution framework marks a major heuristic and algorithmic transition, offering increased flexibility, precision, and control in evolutionary optimization processes, and sparks fundamental questions that bridge self-regulatory generative AI and self-orchestrated evolutionary and developmental biology.