# Geometry-Complete Diffusion for 3D Molecule Generation and Optimization

arXiv: https://arxiv.org/abs/2302.04313 · HTML: https://mlsanity.com/paper/2302.04313/

## Key facts

- Cited by 37 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 44 of its 105 references that are in the map.
- First posted on arXiv 8 Feb 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, 30 of 44)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [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)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [DiffDock: Diffusion Steps, Twists, and Turns for Molecular Docking](https://mlsanity.com/paper/2210.01776/) (2022)
- [Cormorant: Covariant Molecular Neural Networks](https://mlsanity.com/paper/1906.04015/) (2019)
- [Learning Local Equivariant Representations for Large-Scale Atomistic Dynamics](https://mlsanity.com/paper/2204.05249/) (2022)
- [Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densities](https://mlsanity.com/paper/2006.02425/) (2020)
- [What the DAAM: Interpreting Stable Diffusion Using Cross Attention](https://mlsanity.com/paper/2210.04885/) (2022)
- [SE(3) diffusion model with application to protein backbone generation](https://mlsanity.com/paper/2302.02277/) (2023)
- [Pocket2Mol: Efficient Molecular Sampling Based on 3D Protein Pockets](https://mlsanity.com/paper/2205.07249/) (2022)
- [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)

## Built on by (most cited first, 30 of 37)

- [SemlaFlow -- Efficient 3D Molecular Generation with Latent Attention and Equivariant Flow Matching](https://mlsanity.com/paper/2406.07266/) (2024)
- [Diffusion Models in textitDe Novo Drug Design](https://mlsanity.com/paper/2406.08511/) (2024)
- [Geometric Representation Condition Improves Equivariant Molecule Generation](https://mlsanity.com/paper/2410.03655/) (2024)
- [Unified Guidance for Geometry-Conditioned Molecular Generation](https://mlsanity.com/paper/2501.02526/) (2025)
- [GEOM-Drugs Revisited: Toward More Chemically Accurate Benchmarks for 3D Molecule Generation](https://mlsanity.com/paper/2505.00169/) (2025)
- [Scalable Autoregressive 3D Molecule Generation](https://mlsanity.com/paper/2505.13791/) (2025)
- [Controllable Graph Generation with Diffusion Models via Inference-Time Tree Search Guidance](https://mlsanity.com/paper/2510.10402/) (2025)
- [TFG-Flow: Training-free Guidance in Multimodal Generative Flow](https://mlsanity.com/paper/2501.14216/) (2025)
- [SynCoGen: Synthesizable 3D Molecule Generation via Joint Reaction and Coordinate Modeling](https://mlsanity.com/paper/2507.11818/) (2025)
- [DynamicPAE: Generating Scene-Aware Physical Adversarial Examples in Real-Time](https://mlsanity.com/paper/2412.08053/) (2024)
- [Atomic Diffusion Models for Small Molecule Structure Elucidation from NMR Spectra](https://mlsanity.com/paper/2512.03127/) (2025)
- [MolGuidance: Advanced Guidance Strategies for Conditional Molecular Generation with Flow Matching](https://mlsanity.com/paper/2512.12198/) (2025)
- [Generative Aerodynamic Design with Diffusion Probabilistic Models](https://mlsanity.com/paper/2409.13328/) (2024)
- [Data Pruning in Generative Diffusion Models](https://mlsanity.com/paper/2411.12523/) (2024)
- [ScaffoldGPT: A Scaffold-based GPT Model for Drug Optimization](https://mlsanity.com/paper/2502.06891/) (2025)
- [Manipulating 3D Molecules in a Fixed-Dimensional E(3)-Equivariant Latent Space](https://mlsanity.com/paper/2506.00771/) (2025)
- [NEAT: Neighborhood-Guided, Efficient, Autoregressive Set Transformer for 3D Molecular Generation](https://mlsanity.com/paper/2512.05844/) (2025)
- [Diffusion-based Evolutionary Optimization for 3D Multi-Objective Molecular Generation](https://mlsanity.com/paper/2505.11037/) (2025)
- [Predictive Feature Caching for Training-free Acceleration of Molecular Geometry Generation](https://mlsanity.com/paper/2510.04646/) (2025)
- [FlexiFlow: decomposable flow matching for generation of flexible molecular ensemble](https://mlsanity.com/paper/2511.17249/) (2025)
- [Boltzmann-Expected Molecular Design with Decoupled Annealing Flows](https://mlsanity.com/paper/2607.19519/) (2026)
- [Response Matching for generating materials and molecules](https://mlsanity.com/paper/2405.09057/) (2024)
- [D3MES: Diffusion Transformer with multihead equivariant self-attention for 3D molecule generation](https://mlsanity.com/paper/2501.07077/) (2025)
- [BSL: A Unified and Generalizable Multitask Learning Platform for Virtual Drug Discovery from Design to Synthesis](https://mlsanity.com/paper/2508.01195/) (2025)
- [IBEX: Information-Bottleneck-EXplored Coarse-to-Fine Molecular Generation under Limited Data](https://mlsanity.com/paper/2508.10775/) (2025)
- [Toward Better Geometric Representations for Molecule Generative Models](https://mlsanity.com/paper/2605.07693/) (2026)
- [Fragment-Masked Diffusion for Molecular Optimization](https://mlsanity.com/paper/2408.09106/) (2024)
- [Diffusion Models at the Drug Discovery Frontier: A Review on Generating Small Molecules versus Therapeutic Peptides](https://mlsanity.com/paper/2511.00209/) (2025)
- [Chemistry-Enhanced Diffusion-Based Framework for Small-to-Large Molecular Conformation Generation](https://mlsanity.com/paper/2511.12182/) (2025)
- [Hierarchy-Guided Topology Latent Flow for Molecular Graph Generation](https://mlsanity.com/paper/2603.27113/) (2026)

## Abstract (arXiv)

Denoising diffusion probabilistic models (DDPMs) have pioneered new state-of-the-art results in disciplines such as computer vision and computational biology for diverse tasks ranging from text-guided image generation to structure-guided protein design. Along this latter line of research, methods have recently been proposed for generating 3D molecules using equivariant graph neural networks (GNNs) within a DDPM framework. However, such methods are unable to learn important geometric properties of 3D molecules, as they adopt molecule-agnostic and non-geometric GNNs as their 3D graph denoising networks, which notably hinders their ability to generate valid large 3D molecules. In this work, we address these gaps by introducing the Geometry-Complete Diffusion Model (GCDM) for 3D molecule generation, which outperforms existing 3D molecular diffusion models by significant margins across conditional and unconditional settings for the QM9 dataset and the larger GEOM-Drugs dataset, respectively, and generates more novel and unique unconditional 3D molecules for the QM9 dataset compared to previous methods. Importantly, we demonstrate that the geometry-complete denoising process of GCDM learned for 3D molecule generation enables the model to generate a significant proportion of valid and energetically-stable large molecules at the scale of GEOM-Drugs, whereas previous methods fail to do so with the features they learn. Additionally, we show that extensions of GCDM can not only effectively design 3D molecules for specific protein pockets but also that GCDM's geometric features can be repurposed to consistently optimize the geometry and chemical composition of existing 3D molecules for molecular stability and property specificity, demonstrating new versatility of molecular diffusion models. Our source code and data are freely available at https://github.com/BioinfoMachineLearning/Bio-Diffusion.