SymmCD: Symmetry-Preserving Crystal Generation with Diffusion Models

2025/02/05 by Daniel Lévy, Daniel Levy, Siba Smarak Panigrahi +14 · 1 voice · 30 citations
Computer Science · Materials Science · Physics and Astronomy · #Crystallization and Solubility Studies #FOS: Computer and information sciences #FOS: Physical sciences #Machine Learning (cs.LG) #Materials Science (cond-mat.mtrl-sci) #cond-mat.mtrl-sci #cs.LG

paper · pdf · doi:10.48550/arxiv.2502.03638

openalex publication_date 2025/02/05 · arxiv published 2025/02/05 · arxiv updated 2025/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Generating novel crystalline materials has the potential to lead to advancements in fields such as electronics, energy storage, and catalysis. The defining characteristic of crystals is their symmetry, which plays a central role in determining their physical properties. However, existing crystal generation methods either fail to generate materials that display the symmetries of real-world crystals, or simply replicate the symmetry information from examples in a database. To address this limitation, we propose SymmCD, a novel diffusion-based generative model that explicitly incorporates crystallographic symmetry into the generative process. We decompose crystals into two components and learn their joint distribution through diffusion: 1) the asymmetric unit, the smallest subset of the crystal which can generate the whole crystal through symmetry transformations, and; 2) the symmetry transformations needed to be applied to each atom in the asymmetric unit. We also use a novel and interpretable representation for these transformations, enabling generalization across different crystallographic symmetry groups. We showcase the competitive performance of SymmCD on a subset of the Materials Project, obtaining diverse and valid crystals with realistic symmetries and predicted properties.

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Discussions

• Symmetry is the fundamental property of crystals, yet generative models don't yield crystals with true symmetries We solved that with SymmCD and can get crystals from any of the 230 space groups Learn [bsky, 1 points, 0 comments]

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