# Graphite: Iterative Generative Modeling of Graphs

arXiv: https://arxiv.org/abs/1803.10459 · HTML: https://mlsanity.com/paper/1803.10459/

## Key facts

- Cited by 112 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Mar 2018.

## Built on by (most cited first, 30 of 112)

- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)
- [Score-based Generative Modeling of Graphs via the System of Stochastic Differential Equations](https://mlsanity.com/paper/2202.02514/) (2022)
- [Permutation Invariant Graph Generation via Score-Based Generative Modeling](https://mlsanity.com/paper/2003.00638/) (2020)
- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (2021)
- [Adversarial Graph Augmentation to Improve Graph Contrastive Learning](https://mlsanity.com/paper/2106.05819/) (2021)
- [D2C: Diffusion-Denoising Models for Few-shot Conditional Generation](https://mlsanity.com/paper/2106.06819/) (2021)
- [Iterative Refinement Graph Neural Network for Antibody Sequence-Structure Co-design](https://mlsanity.com/paper/2110.04624/) (2021)
- [Autoregressive Diffusion Model for Graph Generation](https://mlsanity.com/paper/2307.08849/) (2023)
- [ExplaGraphs: An Explanation Graph Generation Task for Structured Commonsense Reasoning](https://mlsanity.com/paper/2104.07644/) (2021)
- [Multimodal learning with graphs](https://mlsanity.com/paper/2209.03299/) (2022)
- [CLEAR: Generative Counterfactual Explanations on Graphs](https://mlsanity.com/paper/2210.08443/) (2022)
- [The Future is not One-dimensional: Complex Event Schema Induction by Graph Modeling for Event Prediction](https://mlsanity.com/paper/2104.06344/) (2021)
- [Efficient and Scalable Graph Generation through Iterative Local Expansion](https://mlsanity.com/paper/2312.11529/) (2023)
- [A Survey on Graph Diffusion Models: Generative AI in Science for Molecule, Protein and Material](https://mlsanity.com/paper/2304.01565/) (2023)
- [Graph Positional and Structural Encoder](https://mlsanity.com/paper/2307.07107/) (2023)
- [Graph Auto-Encoder Via Neighborhood Wasserstein Reconstruction](https://mlsanity.com/paper/2202.09025/) (2022)
- [Unifying Generation and Prediction on Graphs with Latent Graph Diffusion](https://mlsanity.com/paper/2402.02518/) (2024)
- [Permutation-Invariant Variational Autoencoder for Graph-Level Representation Learning](https://mlsanity.com/paper/2104.09856/) (2021)
- [Unconditional Scene Graph Generation](https://mlsanity.com/paper/2108.05884/) (2021)
- [Modularity-Aware Graph Autoencoders for Joint Community Detection and Link Prediction](https://mlsanity.com/paper/2202.00961/) (2022)
- [Graph Neural Networks for Molecules](https://mlsanity.com/paper/2209.05582/) (2022)
- [NVDiff: Graph Generation through the Diffusion of Node Vectors](https://mlsanity.com/paper/2211.10794/) (2022)
- [Deep Generative Models for Detector Signature Simulation: A Taxonomic Review](https://mlsanity.com/paper/2312.09597/) (2023)
- [Deconvolutional Networks on Graph Data](https://mlsanity.com/paper/2110.15528/) (2021)
- [On the Power of Edge Independent Graph Models](https://mlsanity.com/paper/2111.00048/) (2021)
- [Improving Graph Generation by Restricting Graph Bandwidth](https://mlsanity.com/paper/2301.10857/) (2023)
- [A Simple and Scalable Representation for Graph Generation](https://mlsanity.com/paper/2312.02230/) (2023)
- [Interpretable Molecular Graph Generation via Monotonic Constraints](https://mlsanity.com/paper/2203.00412/) (2022)
- [Generative Models in Decision Making: A Survey](https://mlsanity.com/paper/2502.17100/) (2025)

## Abstract (arXiv)

Graphs are a fundamental abstraction for modeling relational data. However, graphs are discrete and combinatorial in nature, and learning representations suitable for machine learning tasks poses statistical and computational challenges. In this work, we propose Graphite, an algorithmic framework for unsupervised learning of representations over nodes in large graphs using deep latent variable generative models. Our model parameterizes variational autoencoders (VAE) with graph neural networks, and uses a novel iterative graph refinement strategy inspired by low-rank approximations for decoding. On a wide variety of synthetic and benchmark datasets, Graphite outperforms competing approaches for the tasks of density estimation, link prediction, and node classification. Finally, we derive a theoretical connection between message passing in graph neural networks and mean-field variational inference.