The design of materials with tailored properties is crucial for technological progress. However, most deep generative models focus exclusively on perfectly ordered crystals, neglecting the important class of disordered materials. To address this gap, we introduce DMFlow, a generative framework specifically designed for disordered crystals. Our approach introduces a unified representation for ordered, Substitutionally Disordered (SD), and Positionally Disordered (PD) crystals, and employs a flow matching model to jointly generate all structural components. A key innovation is a Riemannian flow matching framework with spherical reparameterization, which ensures physically valid disorder weights on the probability simplex. The vector field is learned by a novel Graph Neural Network (GNN) that incorporates physical symmetries and a specialized message-passing scheme. Finally, a two-stage discretization procedure converts the continuous weights into multi-hot atomic assignments. To support research in this area, we release a benchmark containing SD, PD, and mixed structures curated from the Crystallography Open Database. Experiments on Crystal Structure Prediction (CSP) and De Novo Generation (DNG) tasks demonstrate that DMFlow significantly outperforms state-of-the-art baselines adapted from ordered crystal generation. We hope our work provides a foundation for the AI-driven discovery of disordered materials.

翻译：具有定制化性质的材料设计对技术进步至关重要。然而，大多数深度生成模型仅专注于完美有序的晶体，忽略了无序材料这一重要类别。为填补这一空白，我们提出了DMFlow，一个专门为无序晶体设计的生成框架。我们的方法引入了有序晶体、置换无序晶体和位置无序晶体的统一表示，并采用流匹配模型联合生成所有结构组分。一个关键创新是结合球面重参数化的黎曼流匹配框架，该框架确保概率单纯形上物理有效的无序权重。向量场通过一种新颖的图神经网络学习，该网络融入了物理对称性和专门的消息传递机制。最后，一个两阶段离散化过程将连续权重转换为多热原子分配。为支持该领域的研究，我们发布了一个包含从晶体学开放数据库中精选的置换无序、位置无序及混合结构的基准数据集。在晶体结构预测和从头生成任务上的实验表明，DMFlow显著优于从有序晶体生成方法改编的现有最先进基线。我们希望我们的工作能为人工智能驱动的无序材料发现奠定基础。