Evolvable Conditional Diffusion

This paper presents an evolvable conditional diffusion method such that black-box, non-differentiable multi-physics models, as are common in domains like computational fluid dynamics and electromagnetics, can be effectively used for guiding the generative process to facilitate autonomous scientific discovery. We formulate the guidance as an optimization problem where one optimizes for a desired fitness function through updates to the descriptive statistic for the denoising distribution, and derive an evolution-guided approach from first principles through the lens of probabilistic evolution. Interestingly, the final derived update algorithm is analogous to the update as per common gradient-based guided diffusion models, but without ever having to compute any derivatives. We validate our proposed evolvable diffusion algorithm in two AI for Science scenarios: the automated design of fluidic topology and meta-surface. Results demonstrate that this method effectively generates designs that better satisfy specific optimization objectives without reliance on differentiable proxies, providing an effective means of guidance-based diffusion that can capitalize on the wealth of black-box, non-differentiable multi-physics numerical models common across Science.

@article{wei2025_2506.13834,
  title={ Evolvable Conditional Diffusion },
  author={ Zhao Wei and Chin Chun Ooi and Abhishek Gupta and Jian Cheng Wong and Pao-Hsiung Chiu and Sheares Xue Wen Toh and Yew-Soon Ong },
  journal={arXiv preprint arXiv:2506.13834},
  year={ 2025 }
}