Space Group Equivariant Crystal Diffusion

Accelerating inverse design of crystalline materials with generative models has significant implications for a range of technologies. Unlike other atomic systems, 3D crystals are invariant to discrete groups of isometries called the space groups. Crucially, these space group symmetries are known to heavily influence materials properties. We propose SGEquiDiff, a crystal generative model which naturally handles space group constraints with space group invariant likelihoods. SGEquiDiff consists of an SE(3)-invariant, telescoping discrete sampler of crystal lattices; permutation-invariant, transformer-based autoregressive sampling of Wyckoff positions, elements, and numbers of symmetrically unique atoms; and space group equivariant diffusion of atomic coordinates. We show that space group equivariant vector fields automatically live in the tangent spaces of the Wyckoff positions. SGEquiDiff achieves state-of-the-art performance on standard benchmark datasets as assessed by quantitative proxy metrics and quantum mechanical calculations.

@article{chang2025_2505.10994,
  title={ Space Group Equivariant Crystal Diffusion },
  author={ Rees Chang and Angela Pak and Alex Guerra and Ni Zhan and Nick Richardson and Elif Ertekin and Ryan P. Adams },
  journal={arXiv preprint arXiv:2505.10994},
  year={ 2025 }
}