SLayerGen: a Crystal Generative Model for all Space and Layer Groups

2026-05-07

AI Summary

This work addresses the limitation of existing crystal generation models, which neglect layer-group symmetry and struggle to produce high-quality single- or bilayer two-periodic materials. We propose SLayerGen, the first framework capable of supporting all 80 layer groups, by integrating coarse-to-fine discrete autoregressive lattice generation, a Transformer-driven approach for sampling Wyckoff positions and elements, and a space- and layer-group equivariant diffusion model that rigorously enforces symmetry constraints. To facilitate evaluation, we construct the first high-quality dataset of single- and bilayer materials, correct an inconsistency in diffusion loss under hexagonal fractional coordinates, and introduce tailored evaluation metrics. Experiments demonstrate that SLayerGen significantly outperforms current bulk-phase models in ab initio generation of two-periodic materials while remaining competitive in joint training scenarios.

Abstract

Crystal generative models have shown rapid progress for accelerating the discovery of bulk, periodic materials. However, many material systems such as 2D superconductors, thin film semiconductors, and catalytic surfaces are diperiodic, i.e., aperiodic along one of the lattice directions. These systems are invariant under the layer groups, which are known to influence materials properties yet not considered by existing models. In this paper, we propose SLayerGen, a generative model that produces crystals constrained to be invariant to any space or layer group. SLayerGen consists of coarse-to-fine discrete autoregressive lattice generation; transformer-based autoregressive sampling of Wyckoff positions, elements, and numbers of symmetrically unique atoms; and space or layer group equivariant diffusion of atomic coordinates. For the diffusion component, we corrected an inconsistency in the loss from prior work arising from hexagonal groups being non-orthogonal in fractional coordinates. To facilitate progress in generative modeling of diperiodic materials, we assembled and filtered datasets of monolayers and bilayers, propose relevant evaluation metrics, and developed novel representations for layer group symmetries. For de novo generation of diperiodic materials, SLayerGen achieves consistent performance gains over bulk crystal generative models and is competitive when training jointly on bulk and diperiodic materials.

Problem

• diperiodic materials
• layer groups
• crystal generative models
• symmetry constraints
• 2D materials

Innovation

• layer groups
• crystal generative model
• equivariant diffusion
• diperiodic materials
• Wyckoff positions