# Diffusion probabilistic models enhance variational autoencoder for crystal structure generative modeling

arXiv: https://arxiv.org/abs/2308.02165 · HTML: https://mlsanity.com/paper/2308.02165/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 24 of its 48 references that are in the map.
- First posted on arXiv 4 Aug 2023.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 24 of 24)

- [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)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Strategies for Pre-training Graph Neural Networks](https://mlsanity.com/paper/1905.12265/) (2019)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [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)
- [Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Molecules](https://mlsanity.com/paper/2011.14115/) (2020)
- [3D Equivariant Diffusion for Target-Aware Molecule Generation and Affinity Prediction](https://mlsanity.com/paper/2303.03543/) (2023)
- [Learning Gradient Fields for Molecular Conformation Generation](https://mlsanity.com/paper/2105.03902/) (2021)
- [On the Expressive Power of Geometric Graph Neural Networks](https://mlsanity.com/paper/2301.09308/) (2023)
- [Molecular generative model based on conditional variational autoencoder for de novo molecular design](https://mlsanity.com/paper/1806.05805/) (2018)
- [An invertible crystallographic representation for general inverse design of inorganic crystals with targeted properties](https://mlsanity.com/paper/2005.07609/) (2020)
- [Conditional molecular design with deep generative models](https://mlsanity.com/paper/1805.00108/) (2018)
- [Star-Shaped Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2302.05259/) (2023)
- [Decoding Structure-Spectrum Relationships with Physically Organized Latent Spaces](https://mlsanity.com/paper/2301.04724/) (2023)

## Built on by (most cited first, 17 of 17)

- [A Hitchhiker's Guide to Geometric GNNs for 3D Atomic Systems](https://mlsanity.com/paper/2312.07511/) (2023)
- [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)
- [Crystal-GFN: sampling crystals with desirable properties and constraints](https://mlsanity.com/paper/2310.04925/) (2023)
- [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)
- [CrystalGRW: Generative Modeling of Crystal Structures with Targeted Properties via Geodesic Random Walks](https://mlsanity.com/paper/2501.08998/) (2025)
- [DMFlow: Disordered Materials Generation by Flow Matching](https://mlsanity.com/paper/2602.04734/) (2026)
- [Grand canonical generative diffusion model for crystalline phases and grain boundaries](https://mlsanity.com/paper/2408.15601/) (2024)
- [Contrastive Learning of English Language and Crystal Graphs for Multimodal Representation of Materials Knowledge](https://mlsanity.com/paper/2502.16451/) (2025)
- [QE-Catalytic: A Graph-Language Multimodal Base Model for Relaxed-Energy Prediction in Catalytic Adsorption](https://mlsanity.com/paper/2512.20084/) (2025)
- [Fourier Transformers for Latent Crystallographic Diffusion and Generative Modeling](https://mlsanity.com/paper/2602.12045/) (2026)
- [Unleashing the power of novel conditional generative approaches for new materials discovery](https://mlsanity.com/paper/2411.03156/) (2024)
- [On the Connection Between Diffusion Models and Molecular Dynamics](https://mlsanity.com/paper/2504.03187/) (2025)
- [AtomDiffuser: Time-Aware Degradation Modeling for Drift and Beam Damage in STEM Imaging](https://mlsanity.com/paper/2508.10359/) (2025)
- [Challenges in Non-Polymeric Crystal Structure Prediction: Why a Geometric, Permutation-Invariant Loss is Needed](https://mlsanity.com/paper/2509.00832/) (2025)
- [A generative machine learning model for designing metal hydrides applied to hydrogen storage](https://mlsanity.com/paper/2601.20892/) (2026)

## Abstract (arXiv)

The crystal diffusion variational autoencoder (CDVAE) is a machine learning model that leverages score matching to generate realistic crystal structures that preserve crystal symmetry. In this study, we leverage novel diffusion probabilistic (DP) models to denoise atomic coordinates rather than adopting the standard score matching approach in CDVAE. Our proposed DP-CDVAE model can reconstruct and generate crystal structures whose qualities are statistically comparable to those of the original CDVAE. Furthermore, notably, when comparing the carbon structures generated by the DP-CDVAE model with relaxed structures obtained from density functional theory calculations, we find that the DP-CDVAE generated structures are remarkably closer to their respective ground states. The energy differences between these structures and the true ground states are, on average, 68.1 meV/atom lower than those generated by the original CDVAE. This significant improvement in the energy accuracy highlights the effectiveness of the DP-CDVAE model in generating crystal structures that better represent their ground-state configurations.