Crystalline materials often exhibit a high level of symmetry. However, most generative models do not account for symmetry, but rather model each atom without any constraints on its position or element. We propose a generative model, Wyckoff Diffusion (WyckoffDiff), which generates symmetry-based descriptions of crystals. This is enabled by considering a crystal structure representation that encodes all symmetry, and we design a novel neural network architecture which enables using this representation inside a discrete generative model framework. In addition to respecting symmetry by construction, the discrete nature of our model enables fast generation. We additionally present a new metric, Fr\'echet Wrenformer Distance, which captures the symmetry aspects of the materials generated, and we benchmark WyckoffDiff against recently proposed generative models for crystal generation. As a proof-of-concept study, we use WyckoffDiff to find new materials below the convex hull of thermodynamical stability.
@article{arxiv.2502.06485,
title = {WyckoffDiff -- A Generative Diffusion Model for Crystal Symmetry},
author = {Filip Ekström Kelvinius and Oskar B. Andersson and Abhijith S. Parackal and Dong Qian and Rickard Armiento and Fredrik Lindsten},
journal= {arXiv preprint arXiv:2502.06485},
year = {2025}
}
Comments
Accepted to ICML 2025, official PMLR proceedings can be found at https://proceedings.mlr.press/v267/ekstrom-kelvinius25a.html. Code is available online at https://github.com/httk/wyckoffdiff