WyckoffDiff -- A Generative Diffusion Model for Crystal Symmetry

TL;DR

WyckoffDiff is a novel generative model that encodes crystal symmetry, enabling fast and symmetry-respecting crystal structure generation, and it can discover new thermodynamically stable materials.

Contribution

The paper introduces WyckoffDiff, a symmetry-aware discrete generative model for crystals, and a new metric to evaluate symmetry in generated materials.

Findings

WyckoffDiff generates symmetry-compliant crystal structures efficiently.

The model outperforms existing methods in symmetry preservation.

It successfully identifies new stable materials below the convex hull.

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. As a proof-of-concept study, we use WyckoffDiff to find new materials below the convex hull of thermodynamical stability.