Vector Field Oriented Diffusion Model for Crystal Material Generation
On the map: Diffusion models → Flow matching, time series and science
Abstract (arXiv)
Discovering crystal structures with specific chemical properties has become an increasingly important focus in material science. However, current models are limited in their ability to generate new crystal lattices, as they only consider atomic positions or chemical composition. To address this issue, we propose a probabilistic diffusion model that utilizes a geometrically equivariant GNN to consider atomic positions and crystal lattices jointly. To evaluate the effectiveness of our model, we introduce a new generation metric inspired by Frechet Inception Distance, but based on GNN energy prediction rather than InceptionV3 used in computer vision. In addition to commonly used metrics like validity, which assesses the plausibility of a structure, this new metric offers a more comprehensive evaluation of our model's capabilities. Our experiments on existing benchmarks show the significance of our diffusion model. We also show that our method can effectively learn meaningful representations.
Key facts. Cited by 9 papers in the map (data through 7 Oct 2026). Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. Builds on 19 of its 41 references that are in the map. First posted on arXiv 20 Dec 2023.
Builds on
19 of 41 references.
Closest ancestors · 4
Same direction, newest first
- 2022Structure-based Drug Design with Equivariant Diffusion Models24 Oct
- 2022Equivariant 3D-Conditional Diffusion Models for Molecular Linker Design11 Oct
- 2022Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problem8 Jun
- 2022GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation6 Mar
Other references · 15
- 2020Denoising Diffusion Probabilistic Modelscited by 20,851
- 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
- 2021E(n) Equivariant Graph Neural Networkscited by 951
- 2020GraphAF: a Flow-based Autoregressive Model for Molecular Graph Generationcited by 301
- 2021Crystal Diffusion Variational Autoencoder for Periodic Material Generationcited by 268
- 2021GraphDF: A Discrete Flow Model for Molecular Graph Generationcited by 177
- 2019Symmetry-adapted generation of 3d point sets for the targeted discovery of moleculescited by 171
- 2022Periodic Graph Transformers for Crystal Material Property Predictioncited by 87
- 2020An invertible crystallographic representation for general inverse design of inorganic crystals with targeted propertiescited by 53
- 2019Data-Driven Approach to Encoding and Decoding 3-D Crystal Structurescited by 34
- 2022Physics Guided Deep Learning for Generative Design of Crystal Materials with Symmetry Constraintscited by 30
- 2018Neural Message Passing with Edge Updates for Predicting Properties of Molecules and Materialscited by 21
3 more
Built on by
Citing papers per year: 2024: 2; 2025: 4; 2026: 3.
9 papers.
- 2024Space Group Constrained Crystal Generationcited by 71
- 2025SymmCD: Symmetry-Preserving Crystal Generation with Diffusion Modelscited by 48
- 2025Materials Generation in the Era of Artificial Intelligence: A Comprehensive Surveycited by 9
- 2025Artificial Intelligence and Generative Models for Materials Discovery -- A Reviewcited by 8
- 2026RADAR: Redundancy-Aware Diffusion for Multi-Agent Communication Structure Generationcited by 5
- 2024Diffusion-based Graph Generative Methodscited by 2
- 2025Transport Novelty Distance: A Distributional Metric for Evaluating Material Generative Modelscited by 2
- 2026Fourier Transformers for Latent Crystallographic Diffusion and Generative Modelingcited by 1
- 2026Deep Generative Crystal Structure Prediction: A Benchmark Study and a Controlled Test of Prototype Dependencecited by 0
- 2026Deep Generative Crystal Structure Prediction: A Benchmark Study and a Controlled Test of Prototype Dependence22 Sep 2026
- 2026RADAR: Redundancy-Aware Diffusion for Multi-Agent Communication Structure Generation11 May 2026
- 2026Fourier Transformers for Latent Crystallographic Diffusion and Generative Modeling12 Feb 2026
- 2025Transport Novelty Distance: A Distributional Metric for Evaluating Material Generative Models10 Dec 2025
- 2025Artificial Intelligence and Generative Models for Materials Discovery -- A Review5 Aug 2025
- 2025Materials Generation in the Era of Artificial Intelligence: A Comprehensive Survey22 May 2025
- 2025SymmCD: Symmetry-Preserving Crystal Generation with Diffusion Models5 Feb 2025
- 2024Space Group Constrained Crystal Generation6 Feb 2024
- 2024Diffusion-based Graph Generative Methods28 Jan 2024
Similar, not cited
Close in wording, no citation either way
- 2025Periodic Materials Generation using Text-Guided Joint Diffusion Model
- 2024Generative Inverse Design of Crystal Structures via Diffusion Models with Transformers
- 2026Crystalite: A Lightweight Transformer for Efficient Crystal Modeling
- 2025CrystalGRW: Generative Modeling of Crystal Structures with Targeted Properties via Geodesic Random Walks
- 2023Scalable Diffusion for Materials Generation
- 2025Kinetic Langevin Diffusion for Crystalline Materials Generation
- 2023Crystal Structure Prediction by Joint Equivariant Diffusion
- 2025Equivariant Diffusion for Crystal Structure Prediction