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Vector Field Oriented Diffusion Model for Crystal Material Generation

Astrid Klipfel, Yaël Fregier, Adlane Sayede, Zied Bouraoui

TL;DR

The paper tackles crystal structure generation with fixed composition and variable ratios by introducing a diffusion model that operates on the full crystal geometry (atomic positions and unit cells) using a geometrically equivariant GNN. It advances the field by modeling lattice updates in a torus plus lattice vector space, leveraging $E(3)\times SL_3(\mathbb{Z})$-equivariant networks and an autoencoder framework to learn the reverse diffusion. A new evaluation metric, Frechet ALIGNN Distance (FAD), is proposed to capture distributional similarity across rich material features, complementing traditional validity and EMD metrics. Empirical results on Materials Project data show GemsDiff producing realistic, composition-controlled crystals with improved density and energy distributions, along with robust lattice generation, suggesting practical value for convex-hull sampling and materials discovery.

Abstract

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.

Vector Field Oriented Diffusion Model for Crystal Material Generation

TL;DR

The paper tackles crystal structure generation with fixed composition and variable ratios by introducing a diffusion model that operates on the full crystal geometry (atomic positions and unit cells) using a geometrically equivariant GNN. It advances the field by modeling lattice updates in a torus plus lattice vector space, leveraging -equivariant networks and an autoencoder framework to learn the reverse diffusion. A new evaluation metric, Frechet ALIGNN Distance (FAD), is proposed to capture distributional similarity across rich material features, complementing traditional validity and EMD metrics. Empirical results on Materials Project data show GemsDiff producing realistic, composition-controlled crystals with improved density and energy distributions, along with robust lattice generation, suggesting practical value for convex-hull sampling and materials discovery.

Abstract

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.
Paper Structure (20 sections, 3 theorems, 42 equations, 6 figures, 4 tables, 2 algorithms)

This paper contains 20 sections, 3 theorems, 42 equations, 6 figures, 4 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Works
  3. Background
  4. Crystalline Materials
  5. Probabilistic Diffusion
  6. Diffusion on a Torus with an Equivariant Graph Neural Network
  7. Equivariant Graph Neural Network
  8. Diffusion Process for Crystals
  9. Experiments
  10. Evaluation on Validity, Earth Mover distance (EMD) for Density and Energy
  11. Frechet Distance with ALIGNN (FAD)
  12. Discussion
  13. Conclusion
  14. Equivariant Graph Neural Network
  15. Mapping from Lattice to Vector Space
  16. ...and 5 more sections

Key Result

Lemma 1

$[\mathcal{N}(\mu,\sigma\text{I})]_\mathbb{T}\xrightarrow[\sigma\to+\infty]{}\mathcal{U}(0,1)^d$

Figures (6)

  • Figure 1: Sampling with GemsDiff and Langevin Dynamics
  • Figure 2: Crystals from materials project
  • Figure 3: FAD and diffusion step.
  • Figure 4: FAD for multiple sample sizes
  • Figure 5: Density ($g.cm^{-3}$) distribution over the generated structure set
  • ...and 1 more figures

Theorems & Definitions (3)

  • Lemma 1
  • Lemma 2
  • Lemma 3