WyckoffDiff – A Generative Diffusion Model for Crystal Symmetry

Filip Ekström Kelvinius, Oskar B. Andersson, Abhijith S Parackal, Dong Qian, Rickard Armiento, Fredrik Lindsten
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:15130-15147, 2025.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-ekstrom-kelvinius25a, title = {{W}yckoff{D}iff – A Generative Diffusion Model for Crystal Symmetry}, author = {Ekstr\"{o}m Kelvinius, Filip and Andersson, Oskar B. and Parackal, Abhijith S and Qian, Dong and Armiento, Rickard and Lindsten, Fredrik}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {15130--15147}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/ekstrom-kelvinius25a/ekstrom-kelvinius25a.pdf}, url = {https://proceedings.mlr.press/v267/ekstrom-kelvinius25a.html}, 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.} }
Endnote
%0 Conference Paper %T WyckoffDiff – A Generative Diffusion Model for Crystal Symmetry %A Filip Ekström Kelvinius %A Oskar B. Andersson %A Abhijith S Parackal %A Dong Qian %A Rickard Armiento %A Fredrik Lindsten %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-ekstrom-kelvinius25a %I PMLR %P 15130--15147 %U https://proceedings.mlr.press/v267/ekstrom-kelvinius25a.html %V 267 %X 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.
APA
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.

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