# MatterGen: a generative model for inorganic materials design

arXiv: https://arxiv.org/abs/2312.03687 · HTML: https://mlsanity.com/paper/2312.03687/

## Key facts

- Cited by 98 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 104 references that are in the map.
- First posted on arXiv 6 Dec 2023.

## Builds on (most cited first, 21 of 21)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [GemNet: Universal Directional Graph Neural Networks for Molecules](https://mlsanity.com/paper/2106.08903/) (2021)
- [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)
- [Symmetry-adapted generation of 3d point sets for the targeted discovery of molecules](https://mlsanity.com/paper/1906.00957/) (2019)
- [Crystal Structure Prediction by Joint Equivariant Diffusion](https://mlsanity.com/paper/2309.04475/) (2023)
- [Scalable Diffusion for Materials Generation](https://mlsanity.com/paper/2311.09235/) (2023)
- [CrystalGAN: Learning to Discover Crystallographic Structures with Generative Adversarial Networks](https://mlsanity.com/paper/1810.11203/) (2018)
- [Crystal-GFN: sampling crystals with desirable properties and constraints](https://mlsanity.com/paper/2310.04925/) (2023)
- [Towards Predicting Equilibrium Distributions for Molecular Systems with Deep Learning](https://mlsanity.com/paper/2306.05445/) (2023)
- [Large-scale machine-learning-assisted exploration of the whole materials space](https://mlsanity.com/paper/2210.00579/) (2022)

## Built on by (most cited first, 30 of 98)

- [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)
- [All-atom Diffusion Transformers: Unified generative modelling of molecules and materials](https://mlsanity.com/paper/2503.03965/) (2025)
- [Space Group Constrained Crystal Generation](https://mlsanity.com/paper/2402.03992/) (2024)
- [Mixed Continuous and Categorical Flow Matching for 3D De Novo Molecule Generation](https://mlsanity.com/paper/2404.19739/) (2024)
- [FlowLLM: Flow Matching for Material Generation with Large Language Models as Base Distributions](https://mlsanity.com/paper/2410.23405/) (2024)
- [Does equivariance matter at scale?](https://mlsanity.com/paper/2410.23179/) (2024)
- [A Fourier Space Perspective on Diffusion Models](https://mlsanity.com/paper/2505.11278/) (2025)
- [SymmCD: Symmetry-Preserving Crystal Generation with Diffusion Models](https://mlsanity.com/paper/2502.03638/) (2025)
- [Training of Physical Neural Networks](https://mlsanity.com/paper/2406.03372/) (2024)
- [LLMatDesign: Autonomous Materials Discovery with Large Language Models](https://mlsanity.com/paper/2406.13163/) (2024)
- [Space Group Informed Transformer for Crystalline Materials Generation](https://mlsanity.com/paper/2403.15734/) (2024)
- [Are LLMs Ready for Real-World Materials Discovery?](https://mlsanity.com/paper/2402.05200/) (2024)
- [Time Series Diffusion in the Frequency Domain](https://mlsanity.com/paper/2402.05933/) (2024)
- [LLaMP: Large Language Model Made Powerful for High-fidelity Materials Knowledge Retrieval and Distillation](https://mlsanity.com/paper/2401.17244/) (2024)
- [A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applications](https://mlsanity.com/paper/2403.00485/) (2024)
- [Universal Physics Transformers: A Framework For Efficiently Scaling Neural Operators](https://mlsanity.com/paper/2402.12365/) (2024)
- [A practical guide to machine learning interatomic potentials -- Status and future](https://mlsanity.com/paper/2503.09814/) (2025)
- [Materials science in the era of large language models: a perspective](https://mlsanity.com/paper/2403.06949/) (2024)
- [FlowMol3: Flow Matching for 3D De Novo Small-Molecule Generation](https://mlsanity.com/paper/2508.12629/) (2025)
- [Action-Minimization Meets Generative Modeling: Efficient Transition Path Sampling with the Onsager-Machlup Functional](https://mlsanity.com/paper/2504.18506/) (2025)
- [MatExpert: Decomposing Materials Discovery by Mimicking Human Experts](https://mlsanity.com/paper/2410.21317/) (2024)
- [MatterChat: A Multi-Modal LLM for Material Science](https://mlsanity.com/paper/2502.13107/) (2025)
- [Flow Density Control: Generative Optimization Beyond Entropy-Regularized Fine-Tuning](https://mlsanity.com/paper/2511.22640/) (2025)
- [A Periodic Bayesian Flow for Material Generation](https://mlsanity.com/paper/2502.02016/) (2025)
- [Periodic Materials Generation using Text-Guided Joint Diffusion Model](https://mlsanity.com/paper/2503.00522/) (2025)
- [Provable Maximum Entropy Manifold Exploration via Diffusion Models](https://mlsanity.com/paper/2506.15385/) (2025)
- [Generative Hierarchical Materials Search](https://mlsanity.com/paper/2409.06762/) (2024)
- [LLM Meets Diffusion: A Hybrid Framework for Crystal Material Generation](https://mlsanity.com/paper/2510.23040/) (2025)
- [Ab Initio Structure Solutions from Nanocrystalline Powder Diffraction Data](https://mlsanity.com/paper/2406.10796/) (2024)

## Abstract (arXiv)

The design of functional materials with desired properties is essential in driving technological advances in areas like energy storage, catalysis, and carbon capture. Generative models provide a new paradigm for materials design by directly generating entirely novel materials given desired property constraints. Despite recent progress, current generative models have low success rate in proposing stable crystals, or can only satisfy a very limited set of property constraints. Here, we present MatterGen, a model that generates stable, diverse inorganic materials across the periodic table and can further be fine-tuned to steer the generation towards a broad range of property constraints. To enable this, we introduce a new diffusion-based generative process that produces crystalline structures by gradually refining atom types, coordinates, and the periodic lattice. We further introduce adapter modules to enable fine-tuning towards any given property constraints with a labeled dataset. Compared to prior generative models, structures produced by MatterGen are more than twice as likely to be novel and stable, and more than 15 times closer to the local energy minimum. After fine-tuning, MatterGen successfully generates stable, novel materials with desired chemistry, symmetry, as well as mechanical, electronic and magnetic properties. Finally, we demonstrate multi-property materials design capabilities by proposing structures that have both high magnetic density and a chemical composition with low supply-chain risk. We believe that the quality of generated materials and the breadth of MatterGen's capabilities represent a major advancement towards creating a universal generative model for materials design.