# MDM: Molecular Diffusion Model for 3D Molecule Generation

arXiv: https://arxiv.org/abs/2209.05710 · HTML: https://mlsanity.com/paper/2209.05710/

## Key facts

- Cited by 58 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 28 references that are in the map.
- First posted on arXiv 13 Sep 2022.

## 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)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (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)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [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)
- [Junction Tree Variational Autoencoder for Molecular Graph Generation](https://mlsanity.com/paper/1802.04364/) (2018)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [MolGAN: An implicit generative model for small molecular graphs](https://mlsanity.com/paper/1805.11973/) (2018)
- [Cormorant: Covariant Molecular Neural Networks](https://mlsanity.com/paper/1906.04015/) (2019)
- [Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densities](https://mlsanity.com/paper/2006.02425/) (2020)
- [GEOM: Energy-annotated molecular conformations for property prediction and molecular generation](https://mlsanity.com/paper/2006.05531/) (2020)
- [A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluation](https://mlsanity.com/paper/1602.03253/) (2016)
- [MoFlow: An Invertible Flow Model for Generating Molecular Graphs](https://mlsanity.com/paper/2006.10137/) (2020)
- [GraphDF: A Discrete Flow Model for Molecular Graph Generation](https://mlsanity.com/paper/2102.01189/) (2021)
- [Symmetry-adapted generation of 3d point sets for the targeted discovery of molecules](https://mlsanity.com/paper/1906.00957/) (2019)
- [E(n) Equivariant Normalizing Flows](https://mlsanity.com/paper/2105.09016/) (2021)
- [Learning Gradient Fields for Molecular Conformation Generation](https://mlsanity.com/paper/2105.03902/) (2021)
- [Syntax-Directed Variational Autoencoder for Structured Data](https://mlsanity.com/paper/1802.08786/) (2018)
- [Molecular geometry prediction using a deep generative graph neural network](https://mlsanity.com/paper/1904.00314/) (2019)
- [An End-to-End Framework for Molecular Conformation Generation via Bilevel Programming](https://mlsanity.com/paper/2105.07246/) (2021)

## Built on by (most cited first, 30 of 58)

- [MiDi: Mixed Graph and 3D Denoising Diffusion for Molecule Generation](https://mlsanity.com/paper/2302.09048/) (2023)
- [Generative Diffusion Models on Graphs: Methods and Applications](https://mlsanity.com/paper/2302.02591/) (2023)
- [Discrete-state Continuous-time Diffusion for Graph Generation](https://mlsanity.com/paper/2405.11416/) (2024)
- [Enhancing Deep Reinforcement Learning: A Tutorial on Generative Diffusion Models in Network Optimization](https://mlsanity.com/paper/2308.05384/) (2023)
- [MUDiff: Unified Diffusion for Complete Molecule Generation](https://mlsanity.com/paper/2304.14621/) (2023)
- [3D molecule generation by denoising voxel grids](https://mlsanity.com/paper/2306.07473/) (2023)
- [A Survey on Graph Diffusion Models: Generative AI in Science for Molecule, Protein and Material](https://mlsanity.com/paper/2304.01565/) (2023)
- [A Survey of Generative AI for de novo Drug Design: New Frontiers in Molecule and Protein Generation](https://mlsanity.com/paper/2402.08703/) (2024)
- [Denoising Diffusion Recommender Model](https://mlsanity.com/paper/2401.06982/) (2024)
- [A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applications](https://mlsanity.com/paper/2403.00485/) (2024)
- [Learning Joint 2D & 3D Diffusion Models for Complete Molecule Generation](https://mlsanity.com/paper/2305.12347/) (2023)
- [Diffusion Models in textitDe Novo Drug Design](https://mlsanity.com/paper/2406.08511/) (2024)
- [Structure-based drug design by denoising voxel grids](https://mlsanity.com/paper/2405.03961/) (2024)
- [NExT-Mol: 3D Diffusion Meets 1D Language Modeling for 3D Molecule Generation](https://mlsanity.com/paper/2502.12638/) (2025)
- [A Practical Guide to Sample-based Statistical Distances for Evaluating Generative Models in Science](https://mlsanity.com/paper/2403.12636/) (2024)
- [Flow Matching Meets Biology and Life Science: A Survey](https://mlsanity.com/paper/2507.17731/) (2025)
- [Distinguished Quantized Guidance for Diffusion-based Sequence Recommendation](https://mlsanity.com/paper/2501.17670/) (2025)
- [Geometric-Facilitated Denoising Diffusion Model for 3D Molecule Generation](https://mlsanity.com/paper/2401.02683/) (2024)
- [DiffSDS: A language diffusion model for protein backbone inpainting under geometric conditions and constraints](https://mlsanity.com/paper/2301.09642/) (2023)
- [ERA-Solver: Error-Robust Adams Solver for Fast Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2301.12935/) (2023)
- [Generative AI and Process Systems Engineering: The Next Frontier](https://mlsanity.com/paper/2402.10977/) (2024)
- [Molecular relaxation by reverse diffusion with time step prediction](https://mlsanity.com/paper/2404.10935/) (2024)
- [DiffGAD: A Diffusion-based Unsupervised Graph Anomaly Detector](https://mlsanity.com/paper/2410.06549/) (2024)
- [Unified Guidance for Geometry-Conditioned Molecular Generation](https://mlsanity.com/paper/2501.02526/) (2025)
- [A Comprehensive Survey on Generative Diffusion Models for Structured Data](https://mlsanity.com/paper/2306.04139/) (2023)
- [Straight-Line Diffusion Model for Efficient 3D Molecular Generation](https://mlsanity.com/paper/2503.02918/) (2025)
- [Siamese Foundation Models for Crystal Structure Prediction](https://mlsanity.com/paper/2503.10471/) (2025)
- [PrefixMol: Target- and Chemistry-aware Molecule Design via Prefix Embedding](https://mlsanity.com/paper/2302.07120/) (2023)
- [Hybrid-Generative Diffusion Models for Attack-Oriented Twin Migration in Vehicular Metaverses](https://mlsanity.com/paper/2407.11036/) (2024)
- [Sampling 3D Molecular Conformers with Diffusion Transformers](https://mlsanity.com/paper/2506.15378/) (2025)

## Abstract (arXiv)

Molecule generation, especially generating 3D molecular geometries from scratch (i.e., 3D textitde novo generation), has become a fundamental task in drug designs. Existing diffusion-based 3D molecule generation methods could suffer from unsatisfactory performances, especially when generating large molecules. At the same time, the generated molecules lack enough diversity. This paper proposes a novel diffusion model to address those two challenges. First, interatomic relations are not in molecules' 3D point cloud representations. Thus, it is difficult for existing generative models to capture the potential interatomic forces and abundant local constraints. To tackle this challenge, we propose to augment the potential interatomic forces and further involve dual equivariant encoders to encode interatomic forces of different strengths. Second, existing diffusion-based models essentially shift elements in geometry along the gradient of data density. Such a process lacks enough exploration in the intermediate steps of the Langevin dynamics. To address this issue, we introduce a distributional controlling variable in each diffusion/reverse step to enforce thorough explorations and further improve generation diversity. Extensive experiments on multiple benchmarks demonstrate that the proposed model significantly outperforms existing methods for both unconditional and conditional generation tasks. We also conduct case studies to help understand the physicochemical properties of the generated molecules.