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

arXiv: https://arxiv.org/abs/2605.08262 · HTML: https://mlsanity.com/paper/2605.08262/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 112 references that are in the map.
- First posted on arXiv 7 May 2026.

## Builds on (most cited first, 30 of 44)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [Crystal Diffusion Variational Autoencoder for Periodic Material Generation](https://mlsanity.com/paper/2110.06197/) (2021)
- [Torsional Diffusion for Molecular Conformer Generation](https://mlsanity.com/paper/2206.01729/) (2022)
- [Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densities](https://mlsanity.com/paper/2006.02425/) (2020)
- [Symmetry-adapted generation of 3d point sets for the targeted discovery of molecules](https://mlsanity.com/paper/1906.00957/) (2019)
- [Frame Averaging for Invariant and Equivariant Network Design](https://mlsanity.com/paper/2110.03336/) (2021)
- [Learning Gradient Fields for Molecular Conformation Generation](https://mlsanity.com/paper/2105.03902/) (2021)
- [Crystal Structure Prediction by Joint Equivariant Diffusion](https://mlsanity.com/paper/2309.04475/) (2023)
- [Universal approximations of invariant maps by neural networks](https://mlsanity.com/paper/1804.10306/) (2018)
- [GraphNorm: A Principled Approach to Accelerating Graph Neural Network Training](https://mlsanity.com/paper/2009.03294/) (2020)
- [Protein structure generation via folding diffusion](https://mlsanity.com/paper/2209.15611/) (2022)
- [FlowMM: Generating Materials with Riemannian Flow Matching](https://mlsanity.com/paper/2406.04713/) (2024)
- [UMA: A Family of Universal Models for Atoms](https://mlsanity.com/paper/2506.23971/) (2025)
- [Fine-Tuned Language Models Generate Stable Inorganic Materials as Text](https://mlsanity.com/paper/2402.04379/) (2024)
- [Residual Pathway Priors for Soft Equivariance Constraints](https://mlsanity.com/paper/2112.01388/) (2021)
- [FAENet: Frame Averaging Equivariant GNN for Materials Modeling](https://mlsanity.com/paper/2305.05577/) (2023)
- [Space Group Constrained Crystal Generation](https://mlsanity.com/paper/2402.03992/) (2024)
- [Scalable Diffusion for Materials Generation](https://mlsanity.com/paper/2311.09235/) (2023)
- [FlowLLM: Flow Matching for Material Generation with Large Language Models as Base Distributions](https://mlsanity.com/paper/2410.23405/) (2024)
- [SymmCD: Symmetry-Preserving Crystal Generation with Diffusion Models](https://mlsanity.com/paper/2502.03638/) (2025)
- [Equivariant Hamiltonian Flows](https://mlsanity.com/paper/1909.13739/) (2019)
- [Data-Driven Approach to Encoding and Decoding 3-D Crystal Structures](https://mlsanity.com/paper/1909.00949/) (2019)
- [Open Materials Generation with Stochastic Interpolants](https://mlsanity.com/paper/2502.02582/) (2025)
- [Wyckoff Transformer: Generation of Symmetric Crystals](https://mlsanity.com/paper/2503.02407/) (2025)
- [WyckoffDiff -- A Generative Diffusion Model for Crystal Symmetry](https://mlsanity.com/paper/2502.06485/) (2025)

## Built on by (most cited first, 2 of 2)

- [OMatG-flash: An All-Atom Flow Map with Reinforce Adjoint Matching for Scalable Materials Discovery](https://mlsanity.com/paper/2609.26402/) (2026)
- [DynaCrys: Crystal Generation with Dynamic Space-Group Diffusion](https://mlsanity.com/paper/2608.07401/) (2026)

## Abstract (arXiv)

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.