# Scalable Diffusion for Materials Generation

arXiv: https://arxiv.org/abs/2311.09235 · HTML: https://mlsanity.com/paper/2311.09235/

## Key facts

- Cited by 54 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 73 references that are in the map.
- First posted on arXiv 18 Oct 2023.

## Builds on (most cited first, 30 of 34)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Zero-Shot Text-to-Image Generation](https://mlsanity.com/paper/2102.12092/) (2021)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Imagen Video: High Definition Video Generation with Diffusion Models](https://mlsanity.com/paper/2210.02303/) (2022)
- [Make-A-Video: Text-to-Video Generation without Text-Video Data](https://mlsanity.com/paper/2209.14792/) (2022)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation](https://mlsanity.com/paper/1606.06650/) (2016)
- [Scaling Autoregressive Models for Content-Rich Text-to-Image Generation](https://mlsanity.com/paper/2206.10789/) (2022)
- [PaLM 2 Technical Report](https://mlsanity.com/paper/2305.10403/) (2023)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Diffusion Probabilistic Models for 3D Point Cloud Generation](https://mlsanity.com/paper/2103.01458/) (2021)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equations](https://mlsanity.com/paper/2202.02514/) (2022)
- [Permutation Invariant Graph Generation via Score-Based Generative Modeling](https://mlsanity.com/paper/2003.00638/) (2020)
- [Crystal Diffusion Variational Autoencoder for Periodic Material Generation](https://mlsanity.com/paper/2110.06197/) (2021)
- [SE(3) diffusion model with application to protein backbone generation](https://mlsanity.com/paper/2302.02277/) (2023)
- [VEEGAN: Reducing Mode Collapse in GANs using Implicit Variational Learning](https://mlsanity.com/paper/1705.07761/) (2017)
- [GeoMol: Torsional Geometric Generation of Molecular 3D Conformer Ensembles](https://mlsanity.com/paper/2106.07802/) (2021)
- [A Conditional Point Diffusion-Refinement Paradigm for 3D Point Cloud Completion](https://mlsanity.com/paper/2112.03530/) (2021)
- [Language models can generate molecules, materials, and protein binding sites directly in three dimensions as XYZ, CIF, and PDB files](https://mlsanity.com/paper/2305.05708/) (2023)
- [An invertible crystallographic representation for general inverse design of inorganic crystals with targeted properties](https://mlsanity.com/paper/2005.07609/) (2020)
- [Generative adversarial networks (GAN) based efficient sampling of chemical space for inverse design of inorganic materials](https://mlsanity.com/paper/1911.05020/) (2019)

## Built on by (most cited first, 30 of 54)

- [FlowMM: Generating Materials with Riemannian Flow Matching](https://mlsanity.com/paper/2406.04713/) (2024)
- [MatterGen: a generative model for inorganic materials design](https://mlsanity.com/paper/2312.03687/) (2023)
- [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)
- [EM Distillation for One-step Diffusion Models](https://mlsanity.com/paper/2405.16852/) (2024)
- [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)
- [Accelerating Diffusion Models with Parallel Sampling: Inference at Sub-Linear Time Complexity](https://mlsanity.com/paper/2405.15986/) (2024)
- [Improving GFlowNets for Text-to-Image Diffusion Alignment](https://mlsanity.com/paper/2406.00633/) (2024)
- [A practical guide to machine learning interatomic potentials -- Status and future](https://mlsanity.com/paper/2503.09814/) (2025)
- [LeMat-GenBench: A Unified Evaluation Framework for Crystal Generative Models](https://mlsanity.com/paper/2512.04562/) (2025)
- [MatExpert: Decomposing Materials Discovery by Mimicking Human Experts](https://mlsanity.com/paper/2410.21317/) (2024)
- [Structure-based out-of-distribution (OOD) materials property prediction: a benchmark study](https://mlsanity.com/paper/2401.08032/) (2024)
- [Images that Sound: Composing Images and Sounds on a Single Canvas](https://mlsanity.com/paper/2405.12221/) (2024)
- [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)
- [Space Group Equivariant Crystal Diffusion](https://mlsanity.com/paper/2505.10994/) (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)
- [Materials Generation in the Era of Artificial Intelligence: A Comprehensive Survey](https://mlsanity.com/paper/2505.16379/) (2025)
- [Crystalite: A Lightweight Transformer for Efficient Crystal Modeling](https://mlsanity.com/paper/2604.02270/) (2026)
- [Flow Matching for Accelerated Simulation of Atomic Transport in Crystalline Materials](https://mlsanity.com/paper/2410.01464/) (2024)
- [Establishing baselines for generative discovery of inorganic crystals](https://mlsanity.com/paper/2501.02144/) (2025)
- [Symmetry-Aware Bayesian Flow Networks for Crystal Generation](https://mlsanity.com/paper/2502.03146/) (2025)
- [Kinetic Langevin Diffusion for Crystalline Materials Generation](https://mlsanity.com/paper/2507.03602/) (2025)
- [AdsorbDiff: Adsorbate Placement via Conditional Denoising Diffusion](https://mlsanity.com/paper/2405.03962/) (2024)
- [Open Materials Generation with Inference-Time Reinforcement Learning](https://mlsanity.com/paper/2602.00424/) (2026)
- [Generative Inverse Design of Crystal Structures via Diffusion Models with Transformers](https://mlsanity.com/paper/2406.09263/) (2024)
- [Known Unknowns: Out-of-Distribution Property Prediction in Materials and Molecules](https://mlsanity.com/paper/2502.05970/) (2025)

## Abstract (arXiv)

Generative models trained on internet-scale data are capable of generating novel and realistic texts, images, and videos. A natural next question is whether these models can advance science, for example by generating novel stable materials. Traditionally, models with explicit structures (e.g., graphs) have been used in modeling structural relationships in scientific data (e.g., atoms and bonds in crystals), but generating structures can be difficult to scale to large and complex systems. Another challenge in generating materials is the mismatch between standard generative modeling metrics and downstream applications. For instance, common metrics such as the reconstruction error do not correlate well with the downstream goal of discovering stable materials. In this work, we tackle the scalability challenge by developing a unified crystal representation that can represent any crystal structure (UniMat), followed by training a diffusion probabilistic model on these UniMat representations. Our empirical results suggest that despite the lack of explicit structure modeling, UniMat can generate high fidelity crystal structures from larger and more complex chemical systems, outperforming previous graph-based approaches under various generative modeling metrics. To better connect the generation quality of materials to downstream applications, such as discovering novel stable materials, we propose additional metrics for evaluating generative models of materials, including per-composition formation energy and stability with respect to convex hulls through decomposition energy from Density Function Theory (DFT). Lastly, we show that conditional generation with UniMat can scale to previously established crystal datasets with up to millions of crystals structures, outperforming random structure search (the current leading method for structure discovery) in discovering new stable materials.