Papers › WyckoffDiff -- A Generative Diffusion Model for Crystal Symmetry

WyckoffDiff -- A Generative Diffusion Model for Crystal Symmetry

10 Feb 2025arXiv:2502.06485archive 2025-07-28

Filip Ekström Kelvinius, Oskar B. Andersson, Abhijith S. Parackal, Dong Qian, Rickard Armiento, Fredrik Lindsten

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.

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