# MoFlow: An Invertible Flow Model for Generating Molecular Graphs

arXiv: https://arxiv.org/abs/2006.10137 · HTML: https://mlsanity.com/paper/2006.10137/

## Key facts

- Cited by 185 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jun 2020.

## Built on by (most cited first, 30 of 185)

- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equations](https://mlsanity.com/paper/2202.02514/) (2022)
- [Large Language Models on Graphs: A Comprehensive Survey](https://mlsanity.com/paper/2312.02783/) (2023)
- [Geometric Latent Diffusion Models for 3D Molecule Generation](https://mlsanity.com/paper/2305.01140/) (2023)
- [Self-Supervised Learning of Graph Neural Networks: A Unified Review](https://mlsanity.com/paper/2102.10757/) (2021)
- [Graph neural networks for materials science and chemistry](https://mlsanity.com/paper/2208.09481/) (2022)
- [GraphDF: A Discrete Flow Model for Molecular Graph Generation](https://mlsanity.com/paper/2102.01189/) (2021)
- [A Molecular Multimodal Foundation Model Associating Molecule Graphs with Natural Language](https://mlsanity.com/paper/2209.05481/) (2022)
- [MARS: Markov Molecular Sampling for Multi-objective Drug Discovery](https://mlsanity.com/paper/2103.10432/) (2021)
- [Generating 3D Molecules for Target Protein Binding](https://mlsanity.com/paper/2204.09410/) (2022)
- [Exploring Chemical Space with Score-based Out-of-distribution Generation](https://mlsanity.com/paper/2206.07632/) (2022)
- [GraphEBM: Molecular Graph Generation with Energy-Based Models](https://mlsanity.com/paper/2102.00546/) (2021)
- [Autoregressive Diffusion Model for Graph Generation](https://mlsanity.com/paper/2307.08849/) (2023)
- [Variational Flow Matching for Graph Generation](https://mlsanity.com/paper/2406.04843/) (2024)
- [Efficient and Degree-Guided Graph Generation via Discrete Diffusion Modeling](https://mlsanity.com/paper/2305.04111/) (2023)
- [Equivariant Energy-Guided SDE for Inverse Molecular Design](https://mlsanity.com/paper/2209.15408/) (2022)
- [A Comprehensive Survey on Deep Graph Representation Learning](https://mlsanity.com/paper/2304.05055/) (2023)
- [A Survey on Deep Graph Generation: Methods and Applications](https://mlsanity.com/paper/2203.06714/) (2022)
- [Molecular Geometry Pretraining with SE(3)-Invariant Denoising Distance Matching](https://mlsanity.com/paper/2206.13602/) (2022)
- [MolGenSurvey: A Systematic Survey in Machine Learning Models for Molecule Design](https://mlsanity.com/paper/2203.14500/) (2022)
- [Efficient Evolutionary Search Over Chemical Space with Large Language Models](https://mlsanity.com/paper/2406.16976/) (2024)
- [Structure-aware Interactive Graph Neural Networks for the Prediction of Protein-Ligand Binding Affinity](https://mlsanity.com/paper/2107.10670/) (2021)
- [Equivariant Flow Matching with Hybrid Probability Transport](https://mlsanity.com/paper/2312.07168/) (2023)
- [MDM: Molecular Diffusion Model for 3D Molecule Generation](https://mlsanity.com/paper/2209.05710/) (2022)
- [DiffBP: Generative Diffusion of 3D Molecules for Target Protein Binding](https://mlsanity.com/paper/2211.11214/) (2022)
- [Graph Generation with Diffusion Mixture](https://mlsanity.com/paper/2302.03596/) (2023)
- [Differentiable Scaffolding Tree for Molecular Optimization](https://mlsanity.com/paper/2109.10469/) (2021)
- [Regression Transformer: Concurrent sequence regression and generation for molecular language modeling](https://mlsanity.com/paper/2202.01338/) (2022)
- [Reinforced Genetic Algorithm for Structure-based Drug Design](https://mlsanity.com/paper/2211.16508/) (2022)
- [Conditional Diffusion Based on Discrete Graph Structures for Molecular Graph Generation](https://mlsanity.com/paper/2301.00427/) (2023)

## Abstract (arXiv)

Generating molecular graphs with desired chemical properties driven by deep graph generative models provides a very promising way to accelerate drug discovery process. Such graph generative models usually consist of two steps: learning latent representations and generation of molecular graphs. However, to generate novel and chemically-valid molecular graphs from latent representations is very challenging because of the chemical constraints and combinatorial complexity of molecular graphs. In this paper, we propose MoFlow, a flow-based graph generative model to learn invertible mappings between molecular graphs and their latent representations. To generate molecular graphs, our MoFlow first generates bonds (edges) through a Glow based model, then generates atoms (nodes) given bonds by a novel graph conditional flow, and finally assembles them into a chemically valid molecular graph with a posthoc validity correction. Our MoFlow has merits including exact and tractable likelihood training, efficient one-pass embedding and generation, chemical validity guarantees, 100% reconstruction of training data, and good generalization ability. We validate our model by four tasks: molecular graph generation and reconstruction, visualization of the continuous latent space, property optimization, and constrained property optimization. Our MoFlow achieves state-of-the-art performance, which implies its potential efficiency and effectiveness to explore large chemical space for drug discovery.