# An Equivariant Generative Framework for Molecular Graph-Structure Co-Design

arXiv: https://arxiv.org/abs/2304.12436 · HTML: https://mlsanity.com/paper/2304.12436/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 94 references that are in the map.
- First posted on arXiv 12 Apr 2023.

## Builds on (most cited first, 30 of 43)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [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)
- [MolGAN: An implicit generative model for small molecular graphs](https://mlsanity.com/paper/1805.11973/) (2018)
- [Graph Convolutional Policy Network for Goal-Directed Molecular Graph Generation](https://mlsanity.com/paper/1806.02473/) (2018)
- [GraphAF: a Flow-based Autoregressive Model for Molecular Graph Generation](https://mlsanity.com/paper/2001.09382/) (2020)
- [Grammar Variational Autoencoder](https://mlsanity.com/paper/1703.01925/) (2017)
- [Pre-training Molecular Graph Representation with 3D Geometry](https://mlsanity.com/paper/2110.07728/) (2021)
- [Hierarchical Generation of Molecular Graphs using Structural Motifs](https://mlsanity.com/paper/2002.03230/) (2020)
- [ChemRL-GEM: Geometry Enhanced Molecular Representation Learning for Property Prediction](https://mlsanity.com/paper/2106.06130/) (2021)
- [MoFlow: An Invertible Flow Model for Generating Molecular Graphs](https://mlsanity.com/paper/2006.10137/) (2020)
- [Pocket2Mol: Efficient Molecular Sampling Based on 3D Protein Pockets](https://mlsanity.com/paper/2205.07249/) (2022)
- [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)
- [Motif-based Graph Self-Supervised Learning for Molecular Property Prediction](https://mlsanity.com/paper/2110.00987/) (2021)
- [A 3D Generative Model for Structure-Based Drug Design](https://mlsanity.com/paper/2203.10446/) (2022)
- [Backdoor Attacks to Graph Neural Networks](https://mlsanity.com/paper/2006.11165/) (2020)
- [GraphNVP: An Invertible Flow Model for Generating Molecular Graphs](https://mlsanity.com/paper/1905.11600/) (2019)
- [GeoMol: Torsional Geometric Generation of Molecular 3D Conformer Ensembles](https://mlsanity.com/paper/2106.07802/) (2021)
- [Generating 3D Molecules for Target Protein Binding](https://mlsanity.com/paper/2204.09410/) (2022)
- [MiDi: Mixed Graph and 3D Denoising Diffusion for Molecule Generation](https://mlsanity.com/paper/2302.09048/) (2023)
- [ProtGNN: Towards Self-Explaining Graph Neural Networks](https://mlsanity.com/paper/2112.00911/) (2021)
- [Inverse design of 3d molecular structures with conditional generative neural networks](https://mlsanity.com/paper/2109.04824/) (2021)

## Built on by (most cited first, 10 of 10)

- [MUDiff: Unified Diffusion for Complete Molecule Generation](https://mlsanity.com/paper/2304.14621/) (2023)
- [Learning Subpocket Prototypes for Generalizable Structure-based Drug Design](https://mlsanity.com/paper/2305.13997/) (2023)
- [CONVERT:Contrastive Graph Clustering with Reliable Augmentation](https://mlsanity.com/paper/2308.08963/) (2023)
- [Accelerating 3D Molecule Generation via Jointly Geometric Optimal Transport](https://mlsanity.com/paper/2405.15252/) (2024)
- [GraphXForm: Graph transformer for computer-aided molecular design](https://mlsanity.com/paper/2411.01667/) (2024)
- [Data-Efficient Molecular Generation with Hierarchical Textual Inversion](https://mlsanity.com/paper/2405.02845/) (2024)
- [Geometric Deep Learning for Structure-Based Drug Design: A Survey](https://mlsanity.com/paper/2306.11768/) (2023)
- [Tokenizing 3D Molecule Structure with Quantized Spherical Coordinates](https://mlsanity.com/paper/2412.01564/) (2024)
- [Concept-Driven Deep Learning for Enhanced Protein-Specific Molecular Generation](https://mlsanity.com/paper/2503.08160/) (2025)
- [SHA-256 Infused Embedding-Driven Generative Modeling of High-Energy Molecules in Low-Data Regimes](https://mlsanity.com/paper/2510.25788/) (2025)

## Abstract (arXiv)

Designing molecules with desirable physiochemical properties and functionalities is a long-standing challenge in chemistry, material science, and drug discovery. Recently, machine learning-based generative models have emerged as promising approaches for de novo molecule design. However, further refinement of methodology is highly desired as most existing methods lack unified modeling of 2D topology and 3D geometry information and fail to effectively learn the structure-property relationship for molecule design. Here we present MolCode, a roto-translation equivariant generative framework for underlineMolecular graph-structure underlineCo-design. In MolCode, 3D geometric information empowers the molecular 2D graph generation, which in turn helps guide the prediction of molecular 3D structure. Extensive experimental results show that MolCode outperforms previous methods on a series of challenging tasks including de novo molecule design, targeted molecule discovery, and structure-based drug design. Particularly, MolCode not only consistently generates valid (99.95% Validity) and diverse (98.75% Uniqueness) molecular graphs/structures with desirable properties, but also generate drug-like molecules with high affinity to target proteins (61.8% high-affinity ratio), which demonstrates MolCode's potential applications in material design and drug discovery. Our extensive investigation reveals that the 2D topology and 3D geometry contain intrinsically complementary information in molecule design, and provide new insights into machine learning-based molecule representation and generation.