# MolGrow: A Graph Normalizing Flow for Hierarchical Molecular Generation

arXiv: https://arxiv.org/abs/2106.05856 · HTML: https://mlsanity.com/paper/2106.05856/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 45 references that are in the map.
- First posted on arXiv 3 Feb 2021.

## Builds on (most cited first, 30 of 31)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [Junction Tree Variational Autoencoder for Molecular Graph Generation](https://mlsanity.com/paper/1802.04364/) (2018)
- [GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Models](https://mlsanity.com/paper/1802.08773/) (2018)
- [MolGAN: An implicit generative model for small molecular graphs](https://mlsanity.com/paper/1805.11973/) (2018)
- [GraphVAE: Towards Generation of Small Graphs Using Variational Autoencoders](https://mlsanity.com/paper/1802.03480/) (2018)
- [Graph Convolutional Policy Network for Goal-Directed Molecular Graph Generation](https://mlsanity.com/paper/1806.02473/) (2018)
- [Dynamic Edge-Conditioned Filters in Convolutional Neural Networks on Graphs](https://mlsanity.com/paper/1704.02901/) (2017)
- [GraphAF: a Flow-based Autoregressive Model for Molecular Graph Generation](https://mlsanity.com/paper/2001.09382/) (2020)
- [GuacaMol: Benchmarking Models for De Novo Molecular Design](https://mlsanity.com/paper/1811.09621/) (2018)
- [Grammar Variational Autoencoder](https://mlsanity.com/paper/1703.01925/) (2017)
- [Molecular Sets (MOSES): A Benchmarking Platform for Molecular Generation Models](https://mlsanity.com/paper/1811.12823/) (2018)
- [Stabilizing Transformers for Reinforcement Learning](https://mlsanity.com/paper/1910.06764/) (2019)
- [Order Matters: Sequence to sequence for sets](https://mlsanity.com/paper/1511.06391/) (2015)
- [Hierarchical Generation of Molecular Graphs using Structural Motifs](https://mlsanity.com/paper/2002.03230/) (2020)
- [Fr'echet ChemNet Distance: A metric for generative models for molecules in drug discovery](https://mlsanity.com/paper/1803.09518/) (2018)
- [MoFlow: An Invertible Flow Model for Generating Molecular Graphs](https://mlsanity.com/paper/2006.10137/) (2020)
- [Learning to Plan Chemical Syntheses](https://mlsanity.com/paper/1708.04202/) (2017)
- [GraphNVP: An Invertible Flow Model for Generating Molecular Graphs](https://mlsanity.com/paper/1905.11600/) (2019)
- [Syntax-Directed Variational Autoencoder for Structured Data](https://mlsanity.com/paper/1802.08786/) (2018)
- [MolecularRNN: Generating realistic molecular graphs with optimized properties](https://mlsanity.com/paper/1905.13372/) (2019)
- [Attention Guided Graph Convolutional Networks for Relation Extraction](https://mlsanity.com/paper/1906.07510/) (2019)
- [Discrete Flows: Invertible Generative Models of Discrete Data](https://mlsanity.com/paper/1905.10347/) (2019)
- [SMILES Enumeration as Data Augmentation for Neural Network Modeling of Molecules](https://mlsanity.com/paper/1703.07076/) (2017)
- [Emerging Convolutions for Generative Normalizing Flows](https://mlsanity.com/paper/1901.11137/) (2019)
- [Self-Referencing Embedded Strings (SELFIES): A 100% robust molecular string representation](https://mlsanity.com/paper/1905.13741/) (2019)

## Built on by (most cited first, 22 of 22)

- [Efficient and Scalable Graph Generation through Iterative Local Expansion](https://mlsanity.com/paper/2312.11529/) (2023)
- [nach0: Multimodal Natural and Chemical Languages Foundation Model](https://mlsanity.com/paper/2311.12410/) (2023)
- [Coarse-to-Fine: a Hierarchical Diffusion Model for Molecule Generation in 3D](https://mlsanity.com/paper/2305.13266/) (2023)
- [Optimizing OOD Detection in Molecular Graphs: A Novel Approach with Diffusion Models](https://mlsanity.com/paper/2404.15625/) (2024)
- [Target-aware Molecular Graph Generation](https://mlsanity.com/paper/2202.04829/) (2022)
- [Gradual Domain Adaptation via Normalizing Flows](https://mlsanity.com/paper/2206.11492/) (2022)
- [GP-MoLFormer: A Foundation Model For Molecular Generation](https://mlsanity.com/paper/2405.04912/) (2024)
- [Improving Small Molecule Generation using Mutual Information Machine](https://mlsanity.com/paper/2208.09016/) (2022)
- [Discrete Graph Auto-Encoder](https://mlsanity.com/paper/2306.07735/) (2023)
- [MolHF: A Hierarchical Normalizing Flow for Molecular Graph Generation](https://mlsanity.com/paper/2305.08457/) (2023)
- [HiGen: Hierarchical Graph Generative Networks](https://mlsanity.com/paper/2305.19337/) (2023)
- [RGCVAE: Relational Graph Conditioned Variational Autoencoder for Molecule Design](https://mlsanity.com/paper/2305.11699/) (2023)
- [ContextFlow++: Generalist-Specialist Flow-based Generative Models with Mixed-Variable Context Encoding](https://mlsanity.com/paper/2406.00578/) (2024)
- [Backdoor Attacks on Discrete Graph Diffusion Models](https://mlsanity.com/paper/2503.06340/) (2025)
- [Instruction Multi-Constraint Molecular Generation Using a Teacher-Student Large Language Model](https://mlsanity.com/paper/2403.13244/) (2024)
- [An In-depth Summary of Recent Artificial Intelligence Applications in Drug Design](https://mlsanity.com/paper/2110.05478/) (2021)
- [Open-Source Molecular Processing Pipeline for Generating Molecules](https://mlsanity.com/paper/2408.06261/) (2024)
- [Feature-Aware (Hyper)graph Generation via Next-Scale Prediction](https://mlsanity.com/paper/2506.01467/) (2025)
- [MODA: A Unified 3D Diffusion Framework for Multi-Task Target-Aware Molecular Generation](https://mlsanity.com/paper/2507.07201/) (2025)
- [NGTM: Substructure-based Neural Graph Topic Model for Interpretable Graph Generation](https://mlsanity.com/paper/2507.13133/) (2025)
- [NovoMolGen: Rethinking Molecular Language Model Pretraining](https://mlsanity.com/paper/2508.13408/) (2025)
- [Hierarchy-Guided Topology Latent Flow for Molecular Graph Generation](https://mlsanity.com/paper/2603.27113/) (2026)

## Abstract (arXiv)

We propose a hierarchical normalizing flow model for generating molecular graphs. The model produces new molecular structures from a single-node graph by recursively splitting every node into two. All operations are invertible and can be used as plug-and-play modules. The hierarchical nature of the latent codes allows for precise changes in the resulting graph: perturbations in the top layer cause global structural changes, while perturbations in the consequent layers change the resulting molecule marginally. The proposed model outperforms existing generative graph models on the distribution learning task. We also show successful experiments on global and constrained optimization of chemical properties using latent codes of the model.