# Geometric Latent Diffusion Models for 3D Molecule Generation

arXiv: https://arxiv.org/abs/2305.01140 · HTML: https://mlsanity.com/paper/2305.01140/

## Key facts

- Cited by 186 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 49 of its 62 references that are in the map.
- First posted on arXiv 2 May 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 49)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [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)
- [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)
- [Taming Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2012.09841/) (2020)
- [SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations](https://mlsanity.com/paper/2108.01073/) (2021)
- [Generating Diverse High-Fidelity Images with VQ-VAE-2](https://mlsanity.com/paper/1906.00446/) (2019)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Diffusion-LM Improves Controllable Text Generation](https://mlsanity.com/paper/2205.14217/) (2022)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Pixel Recurrent Neural Networks](https://mlsanity.com/paper/1601.06759/) (2016)
- [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)
- [Vector-quantized Image Modeling with Improved VQGAN](https://mlsanity.com/paper/2110.04627/) (2021)
- [Junction Tree Variational Autoencoder for Molecular Graph Generation](https://mlsanity.com/paper/1802.04364/) (2018)
- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [LION: Latent Point Diffusion Models for 3D Shape Generation](https://mlsanity.com/paper/2210.06978/) (2022)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data](https://mlsanity.com/paper/1807.02547/) (2018)
- [Learning from Protein Structure with Geometric Vector Perceptrons](https://mlsanity.com/paper/2009.01411/) (2020)
- [GraphAF: a Flow-based Autoregressive Model for Molecular Graph Generation](https://mlsanity.com/paper/2001.09382/) (2020)
- [Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equations](https://mlsanity.com/paper/2202.02514/) (2022)
- [Cormorant: Covariant Molecular Neural Networks](https://mlsanity.com/paper/1906.04015/) (2019)

## Built on by (most cited first, 30 of 186)

- [Derivative-Free Guidance in Continuous and Discrete Diffusion Models with Soft Value-Based Decoding](https://mlsanity.com/paper/2408.08252/) (2024)
- [TFG: Unified Training-Free Guidance for Diffusion Models](https://mlsanity.com/paper/2409.15761/) (2024)
- [Discrete-state Continuous-time Diffusion for Graph Generation](https://mlsanity.com/paper/2405.11416/) (2024)
- [All-atom Diffusion Transformers: Unified generative modelling of molecules and materials](https://mlsanity.com/paper/2503.03965/) (2025)
- [Equivariant Flow Matching with Hybrid Probability Transport](https://mlsanity.com/paper/2312.07168/) (2023)
- [Minimax Optimality of Score-based Diffusion Models: Beyond the Density Lower Bound Assumptions](https://mlsanity.com/paper/2402.15602/) (2024)
- [Graph Diffusion Transformers for Multi-Conditional Molecular Generation](https://mlsanity.com/paper/2401.13858/) (2024)
- [Efficient Video Diffusion Models via Content-Frame Motion-Latent Decomposition](https://mlsanity.com/paper/2403.14148/) (2024)
- [SemlaFlow -- Efficient 3D Molecular Generation with Latent Attention and Equivariant Flow Matching](https://mlsanity.com/paper/2406.07266/) (2024)
- [3D molecule generation by denoising voxel grids](https://mlsanity.com/paper/2306.07473/) (2023)
- [Equivariant Graph Neural Operator for Modeling 3D Dynamics](https://mlsanity.com/paper/2401.11037/) (2024)
- [UGG: Unified Generative Grasping](https://mlsanity.com/paper/2311.16917/) (2023)
- [A Simple and Effective Reinforcement Learning Method for Text-to-Image Diffusion Fine-tuning](https://mlsanity.com/paper/2503.00897/) (2025)
- [UniGS: Unified Representation for Image Generation and Segmentation](https://mlsanity.com/paper/2312.01985/) (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)
- [A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applications](https://mlsanity.com/paper/2403.00485/) (2024)
- [Scenario Dreamer: Vectorized Latent Diffusion for Generating Driving Simulation Environments](https://mlsanity.com/paper/2503.22496/) (2025)
- [SLEDGE: Synthesizing Driving Environments with Generative Models and Rule-Based Traffic](https://mlsanity.com/paper/2403.17933/) (2024)
- [Diffusion Models in textitDe Novo Drug Design](https://mlsanity.com/paper/2406.08511/) (2024)
- [Unifying Generation and Prediction on Graphs with Latent Graph Diffusion](https://mlsanity.com/paper/2402.02518/) (2024)
- [Training Free Guided Flow Matching with Optimal Control](https://mlsanity.com/paper/2410.18070/) (2024)
- [MOFDiff: Coarse-grained Diffusion for Metal-Organic Framework Design](https://mlsanity.com/paper/2310.10732/) (2023)
- [UniGEM: A Unified Approach to Generation and Property Prediction for Molecules](https://mlsanity.com/paper/2410.10516/) (2024)
- [Hyperbolic Geometric Latent Diffusion Model for Graph Generation](https://mlsanity.com/paper/2405.03188/) (2024)
- [Beyond Euclid: An Illustrated Guide to Modern Machine Learning with Geometric, Topological, and Algebraic Structures](https://mlsanity.com/paper/2407.09468/) (2024)
- [Structure-based drug design by denoising voxel grids](https://mlsanity.com/paper/2405.03961/) (2024)
- [Equivariance via Minimal Frame Averaging for More Symmetries and Efficiency](https://mlsanity.com/paper/2406.07598/) (2024)
- [Unified Generative Modeling of 3D Molecules via Bayesian Flow Networks](https://mlsanity.com/paper/2403.15441/) (2024)
- [Are High-Degree Representations Really Unnecessary in Equivariant Graph Neural Networks?](https://mlsanity.com/paper/2410.11443/) (2024)
- [NExT-Mol: 3D Diffusion Meets 1D Language Modeling for 3D Molecule Generation](https://mlsanity.com/paper/2502.12638/) (2025)

## Abstract (arXiv)

Generative models, especially diffusion models (DMs), have achieved promising results for generating feature-rich geometries and advancing foundational science problems such as molecule design. Inspired by the recent huge success of Stable (latent) Diffusion models, we propose a novel and principled method for 3D molecule generation named Geometric Latent Diffusion Models (GeoLDM). GeoLDM is the first latent DM model for the molecular geometry domain, composed of autoencoders encoding structures into continuous latent codes and DMs operating in the latent space. Our key innovation is that for modeling the 3D molecular geometries, we capture its critical roto-translational equivariance constraints by building a point-structured latent space with both invariant scalars and equivariant tensors. Extensive experiments demonstrate that GeoLDM can consistently achieve better performance on multiple molecule generation benchmarks, with up to 7% improvement for the valid percentage of large biomolecules. Results also demonstrate GeoLDM's higher capacity for controllable generation thanks to the latent modeling. Code is provided at urlhttps://github.com/MinkaiXu/GeoLDM.