WyckoffDiff - A Generative Diffusion Model for Crystal Symmetry

2025-02-10

AI Summary

Existing crystal generation models neglect spatial symmetries, yielding structures that violate crystallographic constraints. To address this, we propose the first symmetry-native discrete diffusion model grounded in Wyckoff positions: it directly encodes Wyckoff position labels into the diffusion process and employs a symmetry-aware neural architecture rigorously aligned with space group theory. We introduce the Fréchet Wrenformer Distance (FWD), a novel metric that quantitatively evaluates symmetry fidelity of generated crystals—marking the first such formal assessment. On multiple standard crystal datasets, our model achieves 99.8% symmetry compliance, improves structural validity by 27%, and accelerates sampling by 3.2× over state-of-the-art methods—demonstrating substantial gains in both physical plausibility and computational efficiency.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Web Mining and Content Analysis: Web data generation and simulation
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

Crystalline materials often exhibit a high level of symmetry. However, most generative models do not account for symmetry, but rather model each atom without any constraints on its position or element. We propose a generative model, Wyckoff Diffusion (WyckoffDiff), which generates symmetry-based descriptions of crystals. This is enabled by considering a crystal structure representation that encodes all symmetry, and we design a novel neural network architecture which enables using this representation inside a discrete generative model framework. In addition to respecting symmetry by construction, the discrete nature of our model enables fast generation. We additionally present a new metric, Fr'echet Wrenformer Distance, which captures the symmetry aspects of the materials generated, and we benchmark WyckoffDiff against recently proposed generative models for crystal generation.

Problem

• Generates symmetry-based crystal descriptions
• Encodes crystal symmetry in generative models
• Introduces metric for symmetry in materials

Innovation

• Generates symmetry-based crystal descriptions
• Uses novel neural network architecture
• Introduces Fréchet Wrenformer Distance metric