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).

翻译：新晶体材料的发现需要能够处理周期性边界条件、晶体学对称性和物理约束，同时可扩展至大型且结构多样的晶胞的生成模型。我们提出了一种倒易空间生成流程，通过截断的物种分辨晶胞密度的傅里叶变换来表示晶体，而非直接对原子坐标进行建模。该表示方法天然具有周期性，允许空间群对称性的简单代数作用，并在生成过程中自然地支持可变的原子多重性，从而解决了基于粒子方法的常见局限性。每个空间维度仅使用九个傅里叶基函数，我们的方法即可重构每个化学物种包含多达108个原子的晶胞。我们通过一个作用于复值傅里叶系数的变换器变分自编码器，以及一个在压缩隐空间中进行生成的隐式扩散模型，实例化了该流程。我们在LeMaterial基准上评估了重构和隐式扩散性能，并在小晶胞体系（每个晶胞≤16个原子）中与基于坐标的基线方法进行了无条件生成对比。