# MolHF: A Hierarchical Normalizing Flow for Molecular Graph Generation

arXiv: https://arxiv.org/abs/2305.08457 · HTML: https://mlsanity.com/paper/2305.08457/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 46 references that are in the map.
- First posted on arXiv 15 May 2023.

## Builds on (most cited first, 30 of 35)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [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)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [CCNet: Criss-Cross Attention for Semantic Segmentation](https://mlsanity.com/paper/1811.11721/) (2018)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [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)
- [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)
- [GraphAF: a Flow-based Autoregressive Model for Molecular Graph Generation](https://mlsanity.com/paper/2001.09382/) (2020)
- [Flow++: Improving Flow-Based Generative Models with Variational Dequantization and Architecture Design](https://mlsanity.com/paper/1902.00275/) (2019)
- [Hierarchical Generation of Molecular Graphs using Structural Motifs](https://mlsanity.com/paper/2002.03230/) (2020)
- [MoFlow: An Invertible Flow Model for Generating Molecular Graphs](https://mlsanity.com/paper/2006.10137/) (2020)
- [GraphDF: A Discrete Flow Model for Molecular Graph Generation](https://mlsanity.com/paper/2102.01189/) (2021)
- [MARS: Markov Molecular Sampling for Multi-objective Drug Discovery](https://mlsanity.com/paper/2103.10432/) (2021)
- [Sample-Efficient Optimization in the Latent Space of Deep Generative Models via Weighted Retraining](https://mlsanity.com/paper/2006.09191/) (2020)
- [Stability](https://mlsanity.com/paper/1310.0150/) (2013)
- [GraphNVP: An Invertible Flow Model for Generating Molecular Graphs](https://mlsanity.com/paper/1905.11600/) (2019)
- [Hierarchical Conditional Flow: A Unified Framework for Image Super-Resolution and Image Rescaling](https://mlsanity.com/paper/2108.05301/) (2021)
- [Understanding and Mitigating Exploding Inverses in Invertible Neural Networks](https://mlsanity.com/paper/2006.09347/) (2020)
- [Molecule Generation by Principal Subgraph Mining and Assembling](https://mlsanity.com/paper/2106.15098/) (2021)
- [Improving black-box optimization in VAE latent space using decoder uncertainty](https://mlsanity.com/paper/2107.00096/) (2021)

## Built on by (most cited first, 6 of 6)

- [HYGENE: A Diffusion-based Hypergraph Generation Method](https://mlsanity.com/paper/2408.16457/) (2024)
- [Graph-structured Small Molecule Drug Discovery Through Deep Learning: Progress, Challenges, and Opportunities](https://mlsanity.com/paper/2502.08975/) (2025)
- [Data-Efficient Molecular Generation with Hierarchical Textual Inversion](https://mlsanity.com/paper/2405.02845/) (2024)
- [MTPNet: Multi-Grained Target Perception for Unified Activity Cliff Prediction](https://mlsanity.com/paper/2506.05427/) (2025)
- [Feature-Aware (Hyper)graph Generation via Next-Scale Prediction](https://mlsanity.com/paper/2506.01467/) (2025)
- [HyperDiffusionFields (HyDiF): Diffusion-Guided Hypernetworks for Learning Implicit Molecular Neural Fields](https://mlsanity.com/paper/2510.18122/) (2025)

## Abstract (arXiv)

Molecular de novo design is a critical yet challenging task in scientific fields, aiming to design novel molecular structures with desired property profiles. Significant progress has been made by resorting to generative models for graphs. However, limited attention is paid to hierarchical generative models, which can exploit the inherent hierarchical structure (with rich semantic information) of the molecular graphs and generate complex molecules of larger size that we shall demonstrate to be difficult for most existing models. The primary challenge to hierarchical generation is the non-differentiable issue caused by the generation of intermediate discrete coarsened graph structures. To sidestep this issue, we cast the tricky hierarchical generation problem over discrete spaces as the reverse process of hierarchical representation learning and propose MolHF, a new hierarchical flow-based model that generates molecular graphs in a coarse-to-fine manner. Specifically, MolHF first generates bonds through a multi-scale architecture, then generates atoms based on the coarsened graph structure at each scale. We demonstrate that MolHF achieves state-of-the-art performance in random generation and property optimization, implying its high capacity to model data distribution. Furthermore, MolHF is the first flow-based model that can be applied to model larger molecules (polymer) with more than 100 heavy atoms. The code and models are available at https://github.com/violet-sto/MolHF.