  Crystal Structure Prediction (CSP) is crucial in various scientific
disciplines. While CSP can be addressed by employing currently-prevailing
generative models (e.g. diffusion models), this task encounters unique
challenges owing to the symmetric geometry of crystal structures -- the
invariance of translation, rotation, and periodicity. To incorporate the above
symmetries, this paper proposes DiffCSP, a novel diffusion model to learn the
structure distribution from stable crystals. To be specific, DiffCSP jointly
generates the lattice and atom coordinates for each crystal by employing a
periodic-E(3)-equivariant denoising model, to better model the crystal
geometry. Notably, different from related equivariant generative approaches,
DiffCSP leverages fractional coordinates other than Cartesian coordinates to
represent crystals, remarkably promoting the diffusion and the generation
process of atom positions. Extensive experiments verify that our DiffCSP
significantly outperforms existing CSP methods, with a much lower computation
cost in contrast to DFT-based methods. Moreover, the superiority of DiffCSP is
also observed when it is extended for ab initio crystal generation.
