WyckoffDiff – A Generative Diffusion Model for Crystal Symmetry

Abstract:

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, Fréchet 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.

Recommended citation: Ekström Kelvinius, F., Andersson, O.B., Parackal, A.S., Qian, D., Armiento, R. & Lindsten, F.. (2025). WyckoffDiff – A Generative Diffusion Model for Crystal Symmetry. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:15130-15147 Available from https://proceedings.mlr.press/v267/ekstrom-kelvinius25a.html.
Download Paper