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This paper introduces a reciprocal-space generative pipeline for crystalline materials, representing crystals via a truncated Fourier transform of the species-resolved unit-cell density. This Fourier representation inherently handles periodic boundary conditions and crystallographic symmetries, while also supporting variable atomic multiplicities. The pipeline is instantiated using a transformer variational autoencoder and a latent diffusion model, demonstrating effective reconstruction and unconditional generation of crystal structures.
Forget struggling with periodic boundaries and atomic coordinates: this generative model crafts crystals directly in Fourier space, unlocking efficient generation of complex unit cells.
The discovery of new crystalline materials calls for generative models that handle periodic boundary conditions, crystallographic symmetries, and physical constraints, while scaling to large and structurally diverse unit cells. We propose a reciprocal-space generative pipeline that represents crystals through a truncated Fourier transform of the species-resolved unit-cell density, rather than modeling atomic coordinates directly. This representation is periodicity-native, admits simple algebraic actions of space-group symmetries, and naturally supports variable atomic multiplicities during generation, addressing a common limitation of particle-based approaches. Using only nine Fourier basis functions per spatial dimension, our approach reconstructs unit cells containing up to 108 atoms per chemical species. We instantiate this pipeline with a transformer variational autoencoder over complex-valued Fourier coefficients, and a latent diffusion model that generates in the compressed latent space. We evaluate reconstruction and latent diffusion on the LeMaterial benchmark and compare unconditional generation against coordinate-based baselines in the small-cell regime ($\leq 16$ atoms per unit cell).
