# DMFlow: Disordered Materials Generation by Flow Matching

arXiv: https://arxiv.org/abs/2602.04734 · HTML: https://mlsanity.com/paper/2602.04734/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 17 of its 48 references that are in the map.
- First posted on arXiv 4 Feb 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 17 of 17)

- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Crystal Diffusion Variational Autoencoder for Periodic Material Generation](https://mlsanity.com/paper/2110.06197/) (2021)
- [Flow Matching on General Geometries](https://mlsanity.com/paper/2302.03660/) (2023)
- [Crystal Structure Prediction by Joint Equivariant Diffusion](https://mlsanity.com/paper/2309.04475/) (2023)
- [FlowMM: Generating Materials with Riemannian Flow Matching](https://mlsanity.com/paper/2406.04713/) (2024)
- [Space Group Constrained Crystal Generation](https://mlsanity.com/paper/2402.03992/) (2024)
- [SymmCD: Symmetry-Preserving Crystal Generation with Diffusion Models](https://mlsanity.com/paper/2502.03638/) (2025)
- [Categorical Flow Matching on Statistical Manifolds](https://mlsanity.com/paper/2405.16441/) (2024)
- [WyckoffDiff -- A Generative Diffusion Model for Crystal Symmetry](https://mlsanity.com/paper/2502.06485/) (2025)
- [Diffusion probabilistic models enhance variational autoencoder for crystal structure generative modeling](https://mlsanity.com/paper/2308.02165/) (2023)
- [A Periodic Bayesian Flow for Material Generation](https://mlsanity.com/paper/2502.02016/) (2025)
- [Reinforcement Fine-Tuning for Materials Design](https://mlsanity.com/paper/2504.02367/) (2025)
- [Symmetry-Aware Bayesian Flow Networks for Crystal Generation](https://mlsanity.com/paper/2502.03146/) (2025)
- [Equivariant Diffusion for Crystal Structure Prediction](https://mlsanity.com/paper/2512.07289/) (2025)
- [Siamese Foundation Models for Crystal Structure Prediction](https://mlsanity.com/paper/2503.10471/) (2025)
- [Open Materials Generation with Inference-Time Reinforcement Learning](https://mlsanity.com/paper/2602.00424/) (2026)

## Built on by (most cited first, 5 of 5)

- [Constraint-Aware Flow Matching: Decision Aligned End-to-End Training for Constrained Sampling](https://mlsanity.com/paper/2605.12754/) (2026)
- [Planar Symmetric Pattern Generation](https://mlsanity.com/paper/2606.02073/) (2026)
- [Representations from Pretrained Machine-Learning Interatomic Potentials as Coarse Coordinates for Material Generation and Evaluation](https://mlsanity.com/paper/2607.28776/) (2026)
- [Reducing Symmetry Increase in Equivariant Neural Networks](https://mlsanity.com/paper/2608.12010/) (2026)
- [EP-Flow: Disordered Crystal Structure Prediction without Site-Level Annotations](https://mlsanity.com/paper/2610.01315/) (2026)

## Abstract (arXiv)

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.