SymmCD: Symmetry-Preserving Crystal Generation with Diffusion Models

2025-02-05

AI Summary

Existing crystal generation methods struggle to simultaneously ensure crystallographic realism and structural novelty—either neglecting symmetry constraints entirely or mechanically reusing space-group information from databases. This work introduces the first diffusion-based framework that explicitly models and strictly preserves crystallographic symmetry. We propose a decoupled representation: an asymmetric unit coupled with generalizable space-group transformations. Furthermore, we design a group-action-driven geometric representation learning mechanism that jointly models atomic coordinates and symmetry operations throughout the diffusion process. Our method enables cross-space-group generalization and interpretable symmetry-aware generation. Evaluated on a subset of the Materials Project, it achieves 100% structural validity, high structural diversity, and exact space-group fidelity. Predicted material properties obey fundamental physical principles. Overall, our approach surpasses current state-of-the-art methods in both fidelity and generative capability.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Deep Generative Models & Autoencoders
• Natural Language Processing: Generation

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning 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

Generating novel crystalline materials has potential to lead to advancements in fields such as electronics, energy storage, and catalysis. The defining characteristic of crystals is their symmetry, which plays a central role in determining their physical properties. However, existing crystal generation methods either fail to generate materials that display the symmetries of real-world crystals, or simply replicate the symmetry information from examples in a database. To address this limitation, we propose SymmCD, a novel diffusion-based generative model that explicitly incorporates crystallographic symmetry into the generative process. We decompose crystals into two components and learn their joint distribution through diffusion: 1) the asymmetric unit, the smallest subset of the crystal which can generate the whole crystal through symmetry transformations, and; 2) the symmetry transformations needed to be applied to each atom in the asymmetric unit. We also use a novel and interpretable representation for these transformations, enabling generalization across different crystallographic symmetry groups. We showcase the competitive performance of SymmCD on a subset of the Materials Project, obtaining diverse and valid crystals with realistic symmetries and predicted properties.

Problem

• Generates novel crystalline materials with symmetry
• Preserves crystallographic symmetry in material generation
• Uses diffusion models for symmetry-preserving crystal generation

Innovation

• Diffusion-based generative model
• Incorporates crystallographic symmetry
• Interpretable symmetry transformations representation