# EDGE++: Improved Training and Sampling of EDGE

arXiv: https://arxiv.org/abs/2310.14441 · HTML: https://mlsanity.com/paper/2310.14441/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 31 references that are in the map.
- First posted on arXiv 22 Oct 2023.

## Builds on (most cited first, 22 of 22)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Models](https://mlsanity.com/paper/1802.08773/) (2018)
- [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)
- [Efficient Graph Generation with Graph Recurrent Attention Networks](https://mlsanity.com/paper/1910.00760/) (2019)
- [Learning Deep Generative Models of Graphs](https://mlsanity.com/paper/1803.03324/) (2018)
- [NetGAN: Generating Graphs via Random Walks](https://mlsanity.com/paper/1803.00816/) (2018)
- [Graph Normalizing Flows](https://mlsanity.com/paper/1905.13177/) (2019)
- [Autoregressive Diffusion Model for Graph Generation](https://mlsanity.com/paper/2307.08849/) (2023)
- [Efficient and Degree-Guided Graph Generation via Discrete Diffusion Modeling](https://mlsanity.com/paper/2305.04111/) (2023)
- [Diffusion Models for Graphs Benefit From Discrete State Spaces](https://mlsanity.com/paper/2210.01549/) (2022)
- [Scalable Deep Generative Modeling for Sparse Graphs](https://mlsanity.com/paper/2006.15502/) (2020)
- [Dirichlet Graph Variational Autoencoder](https://mlsanity.com/paper/2010.04408/) (2020)
- [Stochastic Blockmodels meet Graph Neural Networks](https://mlsanity.com/paper/1905.05738/) (2019)
- [Order Matters: Probabilistic Modeling of Node Sequence for Graph Generation](https://mlsanity.com/paper/2106.06189/) (2021)
- [The impossibility of low rank representations for triangle-rich complex networks](https://mlsanity.com/paper/2003.12635/) (2020)
- [NVDiff: Graph Generation through the Diffusion of Node Vectors](https://mlsanity.com/paper/2211.10794/) (2022)
- [On the Power of Edge Independent Graph Models](https://mlsanity.com/paper/2111.00048/) (2021)
- [Interpretable Node Representation with Attribute Decoding](https://mlsanity.com/paper/2212.01682/) (2022)

## Built on by (most cited first, 3 of 3)

- [Graph Generative Pre-trained Transformer](https://mlsanity.com/paper/2501.01073/) (2025)
- [Graph Defense Diffusion Model](https://mlsanity.com/paper/2501.11568/) (2025)
- [Diffusion-based Graph Generative Methods](https://mlsanity.com/paper/2401.15617/) (2024)

## Abstract (arXiv)

Recently developed deep neural models like NetGAN, CELL, and Variational Graph Autoencoders have made progress but face limitations in replicating key graph statistics on generating large graphs. Diffusion-based methods have emerged as promising alternatives, however, most of them present challenges in computational efficiency and generative performance. EDGE is effective at modeling large networks, but its current denoising approach can be inefficient, often leading to wasted computational resources and potential mismatches in its generation process. In this paper, we propose enhancements to the EDGE model to address these issues. Specifically, we introduce a degree-specific noise schedule that optimizes the number of active nodes at each timestep, significantly reducing memory consumption. Additionally, we present an improved sampling scheme that fine-tunes the generative process, allowing for better control over the similarity between the synthesized and the true network. Our experimental results demonstrate that the proposed modifications not only improve the efficiency but also enhance the accuracy of the generated graphs, offering a robust and scalable solution for graph generation tasks.