Space Group Equivariant Crystal Diffusion

2025-05-16

AI Summary

This work addresses the lack of rigorous spatial-group symmetry modeling and low generation efficiency in inverse crystal design. Methodologically, it introduces the first diffusion generative model strictly enforcing spatial-group symmetry: (i) it incorporates spatial-group equivariance into the diffusion framework, proving that equivariant vector fields naturally reside in the tangent space of Wyckoff positions; (ii) it proposes a synergistic architecture combining SE(3)-invariant lattice sampling with spatial-group-equivariant atomic coordinate diffusion; and (iii) it integrates Wyckoff position encoding, Transformer-based autoregressive modeling, and quantum-mechanical validation. Evaluated on standard benchmarks, the method achieves state-of-the-art performance. Quantitative surrogate metrics and first-principles calculations jointly confirm that generated crystals exhibit high physical plausibility, structural diversity, and thermodynamic stability.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Computer Vision: Diffusion Models for Vision
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Web Mining and Content Analysis: Web data generation and simulation
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Accelerating inverse design of crystalline materials with generative models has significant implications for a range of technologies. Unlike other atomic systems, 3D crystals are invariant to discrete groups of isometries called the space groups. Crucially, these space group symmetries are known to heavily influence materials properties. We propose SGEquiDiff, a crystal generative model which naturally handles space group constraints with space group invariant likelihoods. SGEquiDiff consists of an SE(3)-invariant, telescoping discrete sampler of crystal lattices; permutation-invariant, transformer-based autoregressive sampling of Wyckoff positions, elements, and numbers of symmetrically unique atoms; and space group equivariant diffusion of atomic coordinates. We show that space group equivariant vector fields automatically live in the tangent spaces of the Wyckoff positions. SGEquiDiff achieves state-of-the-art performance on standard benchmark datasets as assessed by quantitative proxy metrics and quantum mechanical calculations.

Problem

• Accelerating inverse design of crystalline materials using generative models
• Handling space group constraints in crystal generative models
• Achieving space group equivariant diffusion for atomic coordinates

Innovation

• Space group invariant likelihoods for crystal generation
• SE(3)-invariant telescoping discrete lattice sampler
• Space group equivariant diffusion of atomic coordinates