# SaGess: Sampling Graph Denoising Diffusion Model for Scalable Graph Generation

arXiv: https://arxiv.org/abs/2306.16827 · HTML: https://mlsanity.com/paper/2306.16827/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 15 of its 27 references that are in the map.
- First posted on arXiv 29 Jun 2023.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 15 of 15)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Models](https://mlsanity.com/paper/1802.08773/) (2018)
- [GraphVAE: Towards Generation of Small Graphs Using Variational Autoencoders](https://mlsanity.com/paper/1802.03480/) (2018)
- [Efficient Graph Generation with Graph Recurrent Attention Networks](https://mlsanity.com/paper/1910.00760/) (2019)
- [Structure-based Drug Design with Equivariant Diffusion Models](https://mlsanity.com/paper/2210.13695/) (2022)
- [NetGAN: Generating Graphs via Random Walks](https://mlsanity.com/paper/1803.00816/) (2018)
- [DECAF: Generating Fair Synthetic Data Using Causally-Aware Generative Networks](https://mlsanity.com/paper/2110.12884/) (2021)
- [A Systematic Survey on Deep Generative Models for Graph Generation](https://mlsanity.com/paper/2007.06686/) (2020)
- [Understanding data augmentation for classification: when to warp?](https://mlsanity.com/paper/1609.08764/) (2016)
- [Diffusion Models for Graphs Benefit From Discrete State Spaces](https://mlsanity.com/paper/2210.01549/) (2022)
- [Deep Graph Generators: A Survey](https://mlsanity.com/paper/2012.15544/) (2020)

## Built on by (most cited first, 13 of 13)

- [Sparse Training of Discrete Diffusion Models for Graph Generation](https://mlsanity.com/paper/2311.02142/) (2023)
- [Unifying Generation and Prediction on Graphs with Latent Graph Diffusion](https://mlsanity.com/paper/2402.02518/) (2024)
- [Optimizing OOD Detection in Molecular Graphs: A Novel Approach with Diffusion Models](https://mlsanity.com/paper/2404.15625/) (2024)
- [Diffusion on Graph: Augmentation of Graph Structure for Node Classification](https://mlsanity.com/paper/2503.12563/) (2025)
- [Prior-Informed Flow Matching for Graph Reconstruction](https://mlsanity.com/paper/2601.22107/) (2026)
- [Do Graph Diffusion Models Accurately Capture and Generate Substructure Distributions?](https://mlsanity.com/paper/2502.02488/) (2025)
- [Flowette: Flow Matching with Graphette Priors for Graph Generation](https://mlsanity.com/paper/2602.23566/) (2026)
- [Diffusion-based Graph Generative Methods](https://mlsanity.com/paper/2401.15617/) (2024)
- [Leveraging Graph Diffusion Models for Network Refinement Tasks](https://mlsanity.com/paper/2311.17856/) (2023)
- [FLAGG: Flexible Autoregressive Graph Generation](https://mlsanity.com/paper/2606.05067/) (2026)
- [Generating Large Semi-Synthetic Graphs of Any Size](https://mlsanity.com/paper/2507.02166/) (2025)
- [FAROS: Fair Graph Generation via Attribute Switching Mechanisms](https://mlsanity.com/paper/2507.03728/) (2025)
- [CoDiffGRN: Rethinking Gene Regulatory Network Inference via the BEELINE-KGC Benchmark and Co-evolutionary Discrete Diffusion](https://mlsanity.com/paper/2607.13120/) (2026)

## Abstract (arXiv)

Over recent years, denoising diffusion generative models have come to be considered as state-of-the-art methods for synthetic data generation, especially in the case of generating images. These approaches have also proved successful in other applications such as tabular and graph data generation. However, due to computational complexity, to this date, the application of these techniques to graph data has been restricted to small graphs, such as those used in molecular modeling. In this paper, we propose SaGess, a discrete denoising diffusion approach, which is able to generate large real-world networks by augmenting a diffusion model (DiGress) with a generalized divide-and-conquer framework. The algorithm is capable of generating larger graphs by sampling a covering of subgraphs of the initial graph in order to train DiGress. SaGess then constructs a synthetic graph using the subgraphs that have been generated by DiGress. We evaluate the quality of the synthetic data sets against several competitor methods by comparing graph statistics between the original and synthetic samples, as well as evaluating the utility of the synthetic data set produced by using it to train a task-driven model, namely link prediction. In our experiments, SaGess, outperforms most of the one-shot state-of-the-art graph generating methods by a significant factor, both on the graph metrics and on the link prediction task.