# Inverse design of 3d molecular structures with conditional generative neural networks

arXiv: https://arxiv.org/abs/2109.04824 · HTML: https://mlsanity.com/paper/2109.04824/

## Key facts

- Cited by 93 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 86 references that are in the map.
- First posted on arXiv 10 Sep 2021.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [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)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densities](https://mlsanity.com/paper/2006.02425/) (2020)
- [Machine Learning Force Fields](https://mlsanity.com/paper/2010.07067/) (2020)
- [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)
- [GeoMol: Torsional Geometric Generation of Molecular 3D Conformer Ensembles](https://mlsanity.com/paper/2106.07802/) (2021)
- [Molecular geometry prediction using a deep generative graph neural network](https://mlsanity.com/paper/1904.00314/) (2019)
- [Learning Neural Generative Dynamics for Molecular Conformation Generation](https://mlsanity.com/paper/2102.10240/) (2021)
- [A Generative Model for Molecular Distance Geometry](https://mlsanity.com/paper/1909.11459/) (2019)
- [An End-to-End Framework for Molecular Conformation Generation via Bilevel Programming](https://mlsanity.com/paper/2105.07246/) (2021)
- [Symmetry-Aware Actor-Critic for 3D Molecular Design](https://mlsanity.com/paper/2011.12747/) (2020)
- [Reinforcement Learning for Molecular Design Guided by Quantum Mechanics](https://mlsanity.com/paper/2002.07717/) (2020)
- [Deep learning for molecular design - a review of the state of the art](https://mlsanity.com/paper/1903.04388/) (2019)
- [Machine Learning Molecular Dynamics for the Simulation of Infrared Spectra](https://mlsanity.com/paper/1705.05907/) (2017)
- [Generating valid Euclidean distance matrices](https://mlsanity.com/paper/1910.03131/) (2019)
- [3DMolNet: A Generative Network for Molecular Structures](https://mlsanity.com/paper/2010.06477/) (2020)
- [TorsionNet: A Reinforcement Learning Approach to Sequential Conformer Search](https://mlsanity.com/paper/2006.07078/) (2020)
- [Generating equilibrium molecules with deep neural networks](https://mlsanity.com/paper/1810.11347/) (2018)
- [Generating stable molecules using imitation and reinforcement learning](https://mlsanity.com/paper/2107.05007/) (2021)

## Built on by (most cited first, 30 of 93)

- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [Crystal Diffusion Variational Autoencoder for Periodic Material Generation](https://mlsanity.com/paper/2110.06197/) (2021)
- [Geometric Latent Diffusion Models for 3D Molecule Generation](https://mlsanity.com/paper/2305.01140/) (2023)
- [Crystal Structure Prediction by Joint Equivariant Diffusion](https://mlsanity.com/paper/2309.04475/) (2023)
- [Equivariant Energy-Guided SDE for Inverse Molecular Design](https://mlsanity.com/paper/2209.15408/) (2022)
- [Space Group Constrained Crystal Generation](https://mlsanity.com/paper/2402.03992/) (2024)
- [A Comprehensive Survey on Deep Graph Representation Learning](https://mlsanity.com/paper/2304.05055/) (2023)
- [MolGenSurvey: A Systematic Survey in Machine Learning Models for Molecule Design](https://mlsanity.com/paper/2203.14500/) (2022)
- [Equivariant Flow Matching with Hybrid Probability Transport](https://mlsanity.com/paper/2312.07168/) (2023)
- [Navigating the Design Space of Equivariant Diffusion-Based Generative Models for De Novo 3D Molecule Generation](https://mlsanity.com/paper/2309.17296/) (2023)
- [Graph Diffusion Transformers for Multi-Conditional Molecular Generation](https://mlsanity.com/paper/2401.13858/) (2024)
- [Space Group Informed Transformer for Crystalline Materials Generation](https://mlsanity.com/paper/2403.15734/) (2024)
- [Structure-based drug design with geometric deep learning](https://mlsanity.com/paper/2210.11250/) (2022)
- [Geometry-Complete Diffusion for 3D Molecule Generation and Optimization](https://mlsanity.com/paper/2302.04313/) (2023)
- [Diffeomorphic Counterfactuals with Generative Models](https://mlsanity.com/paper/2206.05075/) (2022)
- [SchNetPack 2.0: A neural network toolbox for atomistic machine learning](https://mlsanity.com/paper/2212.05517/) (2022)
- [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)
- [Graph Neural Networks for Molecules](https://mlsanity.com/paper/2209.05582/) (2022)
- [Equivariant Shape-Conditioned Generation of 3D Molecules for Ligand-Based Drug Design](https://mlsanity.com/paper/2210.04893/) (2022)
- [Unified Generative Modeling of 3D Molecules via Bayesian Flow Networks](https://mlsanity.com/paper/2403.15441/) (2024)
- [Symphony: Symmetry-Equivariant Point-Centered Spherical Harmonics for 3D Molecule Generation](https://mlsanity.com/paper/2311.16199/) (2023)
- [MOFFlow: Flow Matching for Structure Prediction of Metal-Organic Frameworks](https://mlsanity.com/paper/2410.17270/) (2024)
- [NExT-Mol: 3D Diffusion Meets 1D Language Modeling for 3D Molecule Generation](https://mlsanity.com/paper/2502.12638/) (2025)
- [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)
- [Geometric Representation Condition Improves Equivariant Molecule Generation](https://mlsanity.com/paper/2410.03655/) (2024)
- [Equivariant Neural Diffusion for Molecule Generation](https://mlsanity.com/paper/2506.10532/) (2025)
- [PubChemQC B3LYP/6-31G*//PM6 dataset: the Electronic Structures of 86 Million Molecules using B3LYP/6-31G* calculations](https://mlsanity.com/paper/2305.18454/) (2023)

## Abstract (arXiv)

The rational design of molecules with desired properties is a long-standing challenge in chemistry. Generative neural networks have emerged as a powerful approach to sample novel molecules from a learned distribution. Here, we propose a conditional generative neural network for 3d molecular structures with specified chemical and structural properties. This approach is agnostic to chemical bonding and enables targeted sampling of novel molecules from conditional distributions, even in domains where reference calculations are sparse. We demonstrate the utility of our method for inverse design by generating molecules with specified motifs or composition, discovering particularly stable molecules, and jointly targeting multiple electronic properties beyond the training regime.