DMFlow: Disordered Materials Generation by Flow Matching

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.

💡 Research Summary

The paper “DMFlow: Disordered Materials Generation by Flow Matching” addresses a critical gap in the field of deep generative models for materials: the overwhelming focus on perfectly ordered crystals while neglecting the vast class of disordered materials, which include substitutional disorder (SD) and positional disorder (PD). The authors propose a novel framework, DMFlow, that can generate ordered, SD, PD, and mixed (SPD) crystals within a single unified representation and learning pipeline.

Unified Representation
Each crystallographic site i is described by a tuple (s_i, f_i, w_i, f′_i).

• s_i ∈ Δ^{D‑1} is a probability vector over D atomic species (a one‑hot vector in the ordered limit).
• f_i ∈