# Wyckoff Transformer: Generation of Symmetric Crystals

arXiv: https://arxiv.org/abs/2503.02407 · HTML: https://mlsanity.com/paper/2503.02407/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 64 references that are in the map.
- First posted on arXiv 4 Mar 2025.

## Builds on (most cited first, 13 of 13)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [GFlowNet Foundations](https://mlsanity.com/paper/2111.09266/) (2021)
- [Crystal Diffusion Variational Autoencoder for Periodic Material Generation](https://mlsanity.com/paper/2110.06197/) (2021)
- [Crystal Structure Prediction by Joint Equivariant Diffusion](https://mlsanity.com/paper/2309.04475/) (2023)
- [FlowMM: Generating Materials with Riemannian Flow Matching](https://mlsanity.com/paper/2406.04713/) (2024)
- [Fine-Tuned Language Models Generate Stable Inorganic Materials as Text](https://mlsanity.com/paper/2402.04379/) (2024)
- [Space Group Constrained Crystal Generation](https://mlsanity.com/paper/2402.03992/) (2024)
- [Swallowing the Bitter Pill: Simplified Scalable Conformer Generation](https://mlsanity.com/paper/2311.17932/) (2023)
- [SymmCD: Symmetry-Preserving Crystal Generation with Diffusion Models](https://mlsanity.com/paper/2502.03638/) (2025)
- [Space Group Informed Transformer for Crystalline Materials Generation](https://mlsanity.com/paper/2403.15734/) (2024)
- [Efficient Approximations of Complete Interatomic Potentials for Crystal Property Prediction](https://mlsanity.com/paper/2306.10045/) (2023)
- [Crystal-GFN: sampling crystals with desirable properties and constraints](https://mlsanity.com/paper/2310.04925/) (2023)
- [Unified Model for Crystalline Material Generation](https://mlsanity.com/paper/2306.04510/) (2023)

## Built on by (most cited first, 27 of 27)

- [LeMat-GenBench: A Unified Evaluation Framework for Crystal Generative Models](https://mlsanity.com/paper/2512.04562/) (2025)
- [Space Group Equivariant Crystal Diffusion](https://mlsanity.com/paper/2505.10994/) (2025)
- [PLaID++: A Preference Aligned Language Model for Targeted Inorganic Materials Design](https://mlsanity.com/paper/2509.07150/) (2025)
- [Crystalite: A Lightweight Transformer for Efficient Crystal Modeling](https://mlsanity.com/paper/2604.02270/) (2026)
- [Multimodal Crystal Flow: Any-to-Any Modality Generation for Unified Crystal Modeling](https://mlsanity.com/paper/2602.20210/) (2026)
- [CrystalDiT: A Diffusion Transformer for Crystal Generation](https://mlsanity.com/paper/2508.16614/) (2025)
- [Continuous SUN (Stable, Unique, and Novel) Metric for Generative Modeling of Inorganic Crystals](https://mlsanity.com/paper/2510.12405/) (2025)
- [Zatom-1: Towards a Multimodal Foundation Model for 3D Molecules and Materials](https://mlsanity.com/paper/2602.22251/) (2026)
- [MiAD: Mirage Atom Diffusion for De Novo Crystal Generation](https://mlsanity.com/paper/2511.14426/) (2025)
- [Generative Models for Crystalline Materials](https://mlsanity.com/paper/2511.22652/) (2025)
- [CLOUD: A Scalable and Physics-Informed Foundation Model for Crystal Representation Learning](https://mlsanity.com/paper/2506.17345/) (2025)
- [Towards Agentic Intelligence for Materials Science](https://mlsanity.com/paper/2602.00169/) (2026)
- [Substitution-Based Analysis of Structural Novelty for Generative Models of Materials](https://mlsanity.com/paper/2606.23166/) (2026)
- [AI-Assisted Rapid Crystal Structure Generation Towards a Target Local Environment](https://mlsanity.com/paper/2506.08224/) (2025)
- [SLayerGen: a Crystal Generative Model for all Space and Layer Groups](https://mlsanity.com/paper/2605.08262/) (2026)
- [Fourier Transformers for Latent Crystallographic Diffusion and Generative Modeling](https://mlsanity.com/paper/2602.12045/) (2026)
- [Discovering Crystal Structure Prediction Algorithms with an AI Co-Scientist](https://mlsanity.com/paper/2606.22866/) (2026)
- [OMatG-flash: An All-Atom Flow Map with Reinforce Adjoint Matching for Scalable Materials Discovery](https://mlsanity.com/paper/2609.26402/) (2026)
- [Perspective: Towards sustainable exploration of chemical spaces with machine learning](https://mlsanity.com/paper/2604.00069/) (2026)
- [Generating Symmetric Materials using Latent Flow Matching](https://mlsanity.com/paper/2605.10115/) (2026)
- [LapidaryEngine: Fully Conversational Crystal Generation](https://mlsanity.com/paper/2606.14215/) (2026)
- [Atomistic Language Models Understand and Generate Materials](https://mlsanity.com/paper/2606.21395/) (2026)
- [DynaCrys: Crystal Generation with Dynamic Space-Group Diffusion](https://mlsanity.com/paper/2608.07401/) (2026)
- [Symmetry-Breaking De Novo Crystal Generation via Markovian Jump Diffusion](https://mlsanity.com/paper/2608.13457/) (2026)
- [Autonomous discovery of new structure-plausibility laws for explainable and rapid crystal diagnosis and screening](https://mlsanity.com/paper/2609.01209/) (2026)
- [Topology-Stratified Materials Discovery with A Flow-Based Generative Model](https://mlsanity.com/paper/2609.26547/) (2026)
- [GLASS: Global Latent Aggregation with Slot-based Set Decoding for Scalable All-Atom Crystal Generation](https://mlsanity.com/paper/2609.37158/) (2026)

## Abstract (arXiv)

Crystal symmetry plays a fundamental role in determining its physical, chemical, and electronic properties such as electrical and thermal conductivity, optical and polarization behavior, and mechanical strength. Almost all known crystalline materials have internal symmetry. However, this is often inadequately addressed by existing generative models, making the consistent generation of stable and symmetrically valid crystal structures a significant challenge. We introduce WyFormer, a generative model that directly tackles this by formally conditioning on space group symmetry. It achieves this by using Wyckoff positions as the basis for an elegant, compressed, and discrete structure representation. To model the distribution, we develop a permutation-invariant autoregressive model based on the Transformer encoder and an absence of positional encoding. Extensive experimentation demonstrates WyFormer's compelling combination of attributes: it achieves best-in-class symmetry-conditioned generation, incorporates a physics-motivated inductive bias, produces structures with competitive stability, predicts material properties with competitive accuracy even without atomic coordinates, and exhibits unparalleled inference speed.