DMFlow: Disordered Materials Generation by Flow Matching

2026-02-04

AI Summary

Existing deep generative models struggle to effectively model crystal structures exhibiting compositional or positional disorder. To address this challenge, this work proposes DMFlow, a novel framework that unifies the representation of ordered, compositionally disordered, and positionally disordered crystals for the first time. DMFlow introduces a flow-matching approach on a Riemannian manifold, coupled with spherical reparameterization to ensure physically valid disorder weights. The method integrates symmetry-aware graph neural networks, a message-passing mechanism, and a two-stage discretization strategy to enable efficient joint generation of atomic positions and compositions. Experimental results demonstrate that DMFlow significantly outperforms existing baselines in both crystal structure prediction and de novo generation tasks. Additionally, the authors release the first benchmark dataset encompassing compositional disorder, positional disorder, and hybrid structures.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Computer Vision: Diffusion Models for Vision
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Web data generation and simulation
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications

Abstract

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.

Problem

• disordered materials
• crystal generation
• substitutional disorder
• positional disorder
• materials design

Innovation

• flow matching
• disordered materials
• Riemannian geometry
• graph neural network
• spherical reparameterization