Fourier Transformers for Latent Crystallographic Diffusion and Generative Modeling
This work addresses the need for generative models in materials science to discover new crystalline materials, though it appears incremental as it builds on existing generative techniques with a novel representation.
The paper tackled the problem of generating crystalline materials by proposing a reciprocal-space generative pipeline that uses a truncated Fourier transform of species-resolved unit-cell density, enabling handling of periodic boundary conditions and symmetries while scaling to large unit cells with up to 108 atoms per species. They achieved this by implementing a transformer variational autoencoder and latent diffusion model, evaluating on the LeMaterial benchmark and comparing against coordinate-based baselines for small 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).