# GraphEBM: Molecular Graph Generation with Energy-Based Models

arXiv: https://arxiv.org/abs/2102.00546 · HTML: https://mlsanity.com/paper/2102.00546/

## Key facts

- Cited by 85 papers in the map (data through 14 Oct 2026).
- Builds on 58 of its 87 references that are in the map.
- First posted on arXiv 31 Jan 2021.

## Builds on (most cited first, 30 of 58)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (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)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [MoleculeNet: A Benchmark for Molecular Machine Learning](https://mlsanity.com/paper/1703.00564/) (2017)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [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)
- [Junction Tree Variational Autoencoder for Molecular Graph Generation](https://mlsanity.com/paper/1802.04364/) (2018)
- [Graph U-Nets](https://mlsanity.com/paper/1905.05178/) (2019)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [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)
- [Analyzing Learned Molecular Representations for Property Prediction](https://mlsanity.com/paper/1904.01561/) (2019)
- [Graph Structure Learning for Robust Graph Neural Networks](https://mlsanity.com/paper/2005.10203/) (2020)
- [Graph Convolutional Policy Network for Goal-Directed Molecular Graph Generation](https://mlsanity.com/paper/1806.02473/) (2018)

## Built on by (most cited first, 30 of 85)

- [Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equations](https://mlsanity.com/paper/2202.02514/) (2022)
- [Crystal Diffusion Variational Autoencoder for Periodic Material Generation](https://mlsanity.com/paper/2110.06197/) (2021)
- [Machine Learning for Synthetic Data Generation: A Review](https://mlsanity.com/paper/2302.04062/) (2023)
- [Generating 3D Molecules for Target Protein Binding](https://mlsanity.com/paper/2204.09410/) (2022)
- [SPECTRE: Spectral Conditioning Helps to Overcome the Expressivity Limits of One-shot Graph Generators](https://mlsanity.com/paper/2204.01613/) (2022)
- [Exploring Chemical Space with Score-based Out-of-distribution Generation](https://mlsanity.com/paper/2206.07632/) (2022)
- [Periodic Graph Transformers for Crystal Material Property Prediction](https://mlsanity.com/paper/2209.11807/) (2022)
- [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)
- [DIG: A Turnkey Library for Diving into Graph Deep Learning Research](https://mlsanity.com/paper/2103.12608/) (2021)
- [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)
- [DiffBP: Generative Diffusion of 3D Molecules for Target Protein Binding](https://mlsanity.com/paper/2211.11214/) (2022)
- [Differentiable Scaffolding Tree for Molecular Optimization](https://mlsanity.com/paper/2109.10469/) (2021)
- [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)
- [Top-N: Equivariant set and graph generation without exchangeability](https://mlsanity.com/paper/2110.02096/) (2021)
- [Fast Graph Generation via Spectral Diffusion](https://mlsanity.com/paper/2211.08892/) (2022)
- [Complete and Efficient Graph Transformers for Crystal Material Property Prediction](https://mlsanity.com/paper/2403.11857/) (2024)
- [Genetic algorithms are strong baselines for molecule generation](https://mlsanity.com/paper/2310.09267/) (2023)
- [Bringing Your Own View: Graph Contrastive Learning without Prefabricated Data Augmentations](https://mlsanity.com/paper/2201.01702/) (2022)
- [A Latent Diffusion Model for Protein Structure Generation](https://mlsanity.com/paper/2305.04120/) (2023)
- [Towards Symmetry-Aware Generation of Periodic Materials](https://mlsanity.com/paper/2307.02707/) (2023)
- [Controllable Data Generation by Deep Learning: A Review](https://mlsanity.com/paper/2207.09542/) (2022)
- [Learning Energy-Based Models by Cooperative Diffusion Recovery Likelihood](https://mlsanity.com/paper/2309.05153/) (2023)
- [Energy-based Automated Model Evaluation](https://mlsanity.com/paper/2401.12689/) (2024)
- [A Simple and Scalable Representation for Graph Generation](https://mlsanity.com/paper/2312.02230/) (2023)
- [Periodic Materials Generation using Text-Guided Joint Diffusion Model](https://mlsanity.com/paper/2503.00522/) (2025)
- [Machine Learning for a Sustainable Energy Future](https://mlsanity.com/paper/2210.10391/) (2022)

## Abstract (arXiv)

We note that most existing approaches for molecular graph generation fail to guarantee the intrinsic property of permutation invariance, resulting in unexpected bias in generative models. In this work, we propose GraphEBM to generate molecular graphs using energy-based models. In particular, we parameterize the energy function in a permutation invariant manner, thus making GraphEBM permutation invariant. We apply Langevin dynamics to train the energy function by approximately maximizing likelihood and generate samples with low energies. Furthermore, to generate molecules with a desirable property, we propose a simple yet effective strategy, which pushes down energies with flexible degrees according to the properties of corresponding molecules. Finally, we explore the use of GraphEBM for generating molecules with multiple objectives in a compositional manner. Comprehensive experimental results on random, goal-directed, and compositional generation tasks demonstrate the effectiveness of our proposed method.