# Graph Residual Flow for Molecular Graph Generation

arXiv: https://arxiv.org/abs/1909.13521 · HTML: https://mlsanity.com/paper/1909.13521/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Sep 2019.

## Built on by (most cited first, 23 of 23)

- [GraphDF: A Discrete Flow Model for Molecular Graph Generation](https://mlsanity.com/paper/2102.01189/) (2021)
- [GraphEBM: Molecular Graph Generation with Energy-Based Models](https://mlsanity.com/paper/2102.00546/) (2021)
- [A Survey on Deep Graph Generation: Methods and Applications](https://mlsanity.com/paper/2203.06714/) (2022)
- [MolGenSurvey: A Systematic Survey in Machine Learning Models for Molecule Design](https://mlsanity.com/paper/2203.14500/) (2022)
- [Differentiable Scaffolding Tree for Molecular Optimization](https://mlsanity.com/paper/2109.10469/) (2021)
- [Artificial Intelligence in Drug Discovery: Applications and Techniques](https://mlsanity.com/paper/2106.05386/) (2021)
- [Data-centric Graph Learning: A Survey](https://mlsanity.com/paper/2310.04987/) (2023)
- [Target-aware Molecular Graph Generation](https://mlsanity.com/paper/2202.04829/) (2022)
- [Modular Flows: Differential Molecular Generation](https://mlsanity.com/paper/2210.06032/) (2022)
- [LLM-Based Multi-Agent Systems are Scalable Graph Generative Models](https://mlsanity.com/paper/2410.09824/) (2024)
- [FastFlows: Flow-Based Models for Molecular Graph Generation](https://mlsanity.com/paper/2201.12419/) (2022)
- [Conditional β-VAE for De Novo Molecular Generation](https://mlsanity.com/paper/2205.01592/) (2022)
- [Molecule Design by Latent Space Energy-Based Modeling and Gradual Distribution Shifting](https://mlsanity.com/paper/2306.14902/) (2023)
- [Gradient GA: Gradient Genetic Algorithm for Drug Molecular Design](https://mlsanity.com/paper/2502.09860/) (2025)
- [Overcoming Order in Autoregressive Graph Generation](https://mlsanity.com/paper/2402.03387/) (2024)
- [Fine-Grained Traffic Inference from Road to Lane via Spatio-Temporal Graph Node Generation](https://mlsanity.com/paper/2507.19089/) (2025)
- [Large-Scale Auto-Regressive Modeling Of Street Networks](https://mlsanity.com/paper/2209.00281/) (2022)
- [GraphSPNs: Sum-Product Networks Benefit From Canonical Orderings](https://mlsanity.com/paper/2408.09451/) (2024)
- [An In-depth Summary of Recent Artificial Intelligence Applications in Drug Design](https://mlsanity.com/paper/2110.05478/) (2021)
- [HelixMO: Sample-Efficient Molecular Optimization in Scene-Sensitive Latent Space](https://mlsanity.com/paper/2112.00905/) (2021)
- [Physics-integrated generative modeling using attentive planar normalizing flow based variational autoencoder](https://mlsanity.com/paper/2404.12267/) (2024)
- [Hybrid Quantum Generative Adversarial Networks for Molecular Simulation and Drug Discovery](https://mlsanity.com/paper/2212.07826/) (2022)
- [An open unified deep graph learning framework for discovering drug leads](https://mlsanity.com/paper/2301.03424/) (2022)

## Abstract (arXiv)

Statistical generative models for molecular graphs attract attention from many researchers from the fields of bio- and chemo-informatics. Among these models, invertible flow-based approaches are not fully explored yet. In this paper, we propose a powerful invertible flow for molecular graphs, called graph residual flow (GRF). The GRF is based on residual flows, which are known for more flexible and complex non-linear mappings than traditional coupling flows. We theoretically derive non-trivial conditions such that GRF is invertible, and present a way of keeping the entire flows invertible throughout the training and sampling. Experimental results show that a generative model based on the proposed GRF achieves comparable generation performance, with much smaller number of trainable parameters compared to the existing flow-based model.