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.
View on arXiv@article{levy2025_2502.03638,
title={ SymmCD: Symmetry-Preserving Crystal Generation with Diffusion Models },
author={ Daniel Levy and Siba Smarak Panigrahi and Sékou-Oumar Kaba and Qiang Zhu and Kin Long Kelvin Lee and Mikhail Galkin and Santiago Miret and Siamak Ravanbakhsh },
journal={arXiv preprint arXiv:2502.03638},
year={ 2025 }
}