# Evolvable Conditional Diffusion

arXiv: https://arxiv.org/abs/2506.13834 · HTML: https://mlsanity.com/paper/2506.13834/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 42 references that are in the map.
- First posted on arXiv 16 Jun 2025.

## Builds on (most cited first, 28 of 28)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Diffusion-LM Improves Controllable Text Generation](https://mlsanity.com/paper/2205.14217/) (2022)
- [Diffusion Models in Vision: A Survey](https://mlsanity.com/paper/2209.04747/) (2022)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [Evolution Strategies as a Scalable Alternative to Reinforcement Learning](https://mlsanity.com/paper/1703.03864/) (2017)
- [Universal Guidance for Diffusion Models](https://mlsanity.com/paper/2302.07121/) (2023)
- [PhysDiff: Physics-Guided Human Motion Diffusion Model](https://mlsanity.com/paper/2212.02500/) (2022)
- [Derivative-Free Guidance in Continuous and Discrete Diffusion Models with Soft Value-Based Decoding](https://mlsanity.com/paper/2408.08252/) (2024)
- [Equivariant 3D-Conditional Diffusion Models for Molecular Linker Design](https://mlsanity.com/paper/2210.05274/) (2022)
- [End-to-End Diffusion Latent Optimization Improves Classifier Guidance](https://mlsanity.com/paper/2303.13703/) (2023)
- [Guided-TTS: A Diffusion Model for Text-to-Speech via Classifier Guidance](https://mlsanity.com/paper/2111.11755/) (2021)
- [Diffusion Models Beat GANs on Topology Optimization](https://mlsanity.com/paper/2208.09591/) (2022)
- [The Surprising Creativity of Digital Evolution: A Collection of Anecdotes from the Evolutionary Computation and Artificial Life Research Communities](https://mlsanity.com/paper/1803.03453/) (2018)
- [Dirichlet Diffusion Score Model for Biological Sequence Generation](https://mlsanity.com/paper/2305.10699/) (2023)
- [An Overview of Diffusion Models: Applications, Guided Generation, Statistical Rates and Optimization](https://mlsanity.com/paper/2404.07771/) (2024)
- [Uncertainty-aware Surrogate Models for Airfoil Flow Simulations with Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2312.05320/) (2023)
- [Half a Dozen Real-World Applications of Evolutionary Multitasking, and More](https://mlsanity.com/paper/2109.13101/) (2021)
- [Fast Direct: Query-Efficient Online Black-box Guidance for Diffusion-model Target Generation](https://mlsanity.com/paper/2502.01692/) (2025)
- [Chemistry-Inspired Diffusion with Non-Differentiable Guidance](https://mlsanity.com/paper/2410.06502/) (2024)
- [Neuroevolution of Physics-Informed Neural Nets: Benchmark Problems and Comparative Results](https://mlsanity.com/paper/2212.07624/) (2022)
- [Covariance-Adaptive Sequential Black-box Optimization for Diffusion Targeted Generation](https://mlsanity.com/paper/2406.00812/) (2024)

## Built on by (most cited first, 5 of 5)

- [A Plug-and-Play Multi-Criteria Guidance for Diverse In-Betweening Human Motion Generation](https://mlsanity.com/paper/2508.01590/) (2025)
- [Slowly Annealed Langevin Dynamics: Theory and Applications to Training-Free Guided Generation](https://mlsanity.com/paper/2605.07950/) (2026)
- [Evolutionary Computation as Natural Generative AI](https://mlsanity.com/paper/2510.08590/) (2025)
- [Seek and You Shall Fold](https://mlsanity.com/paper/2511.13244/) (2025)
- [Flow-Direct: Feedback-Efficient and Reusable Guidance for Flow Models via Non-Parametric Guidance Field](https://mlsanity.com/paper/2605.16348/) (2026)

## Abstract (arXiv)

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.