# NVDiff: Graph Generation through the Diffusion of Node Vectors

arXiv: https://arxiv.org/abs/2211.10794 · HTML: https://mlsanity.com/paper/2211.10794/

## Key facts

- Cited by 18 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 45 of its 61 references that are in the map.
- First posted on arXiv 19 Nov 2022.

## 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, 30 of 45)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [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)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Junction Tree Variational Autoencoder for Molecular Graph Generation](https://mlsanity.com/paper/1802.04364/) (2018)
- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)
- [WaveGrad: Estimating Gradients for Waveform Generation](https://mlsanity.com/paper/2009.00713/) (2020)
- [GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Models](https://mlsanity.com/paper/1802.08773/) (2018)
- [Flow Network based Generative Models for Non-Iterative Diverse Candidate Generation](https://mlsanity.com/paper/2106.04399/) (2021)
- [GraphVAE: Towards Generation of Small Graphs Using Variational Autoencoders](https://mlsanity.com/paper/1802.03480/) (2018)
- [GraphAF: a Flow-based Autoregressive Model for Molecular Graph Generation](https://mlsanity.com/paper/2001.09382/) (2020)
- [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)
- [Hierarchical Generation of Molecular Graphs using Structural Motifs](https://mlsanity.com/paper/2002.03230/) (2020)
- [Fr'echet ChemNet Distance: A metric for generative models for molecules in drug discovery](https://mlsanity.com/paper/1803.09518/) (2018)
- [Diagnosing and Enhancing VAE Models](https://mlsanity.com/paper/1903.05789/) (2019)
- [Constrained Graph Variational Autoencoders for Molecule Design](https://mlsanity.com/paper/1805.09076/) (2018)
- [MoFlow: An Invertible Flow Model for Generating Molecular Graphs](https://mlsanity.com/paper/2006.10137/) (2020)
- [GraphDF: A Discrete Flow Model for Molecular Graph Generation](https://mlsanity.com/paper/2102.01189/) (2021)
- [E(n) Equivariant Normalizing Flows](https://mlsanity.com/paper/2105.09016/) (2021)
- [Symbolic Music Generation with Diffusion Models](https://mlsanity.com/paper/2103.16091/) (2021)
- [GraphNVP: An Invertible Flow Model for Generating Molecular Graphs](https://mlsanity.com/paper/1905.11600/) (2019)
- [Graphite: Iterative Generative Modeling of Graphs](https://mlsanity.com/paper/1803.10459/) (2018)
- [Graph Normalizing Flows](https://mlsanity.com/paper/1905.13177/) (2019)
- [Multi-Objective De Novo Drug Design with Conditional Graph Generative Model](https://mlsanity.com/paper/1801.07299/) (2018)

## Built on by (most cited first, 18 of 18)

- [Efficient and Degree-Guided Graph Generation via Discrete Diffusion Modeling](https://mlsanity.com/paper/2305.04111/) (2023)
- [A Survey on Graph Diffusion Models: Generative AI in Science for Molecule, Protein and Material](https://mlsanity.com/paper/2304.01565/) (2023)
- [Graph Generative Pre-trained Transformer](https://mlsanity.com/paper/2501.01073/) (2025)
- [Controllable Graph Generation with Diffusion Models via Inference-Time Tree Search Guidance](https://mlsanity.com/paper/2510.10402/) (2025)
- [Enhancing Diffusion-based Point Cloud Generation with Smoothness Constraint](https://mlsanity.com/paper/2404.02396/) (2024)
- [Size Matters: Large Graph Generation with HiGGs](https://mlsanity.com/paper/2306.11412/) (2023)
- [EDGE++: Improved Training and Sampling of EDGE](https://mlsanity.com/paper/2310.14441/) (2023)
- [Modeling and design of heterogeneous hierarchical bioinspired spider web structures using generative deep learning and additive manufacturing](https://mlsanity.com/paper/2304.05137/) (2023)
- [Diffusion-based Graph Generative Methods](https://mlsanity.com/paper/2401.15617/) (2024)
- [Latent Conditional Diffusion-based Data Augmentation for Continuous-Time Dynamic Graph Model](https://mlsanity.com/paper/2407.08500/) (2024)
- [Inference Attacks Against Graph Generative Diffusion Models](https://mlsanity.com/paper/2601.03701/) (2026)
- [SANGEA: Scalable and Attributed Network Generation](https://mlsanity.com/paper/2309.15648/) (2023)
- [DMol: A Highly Efficient and Chemical Motif-Preserving Molecule Generation Platform](https://mlsanity.com/paper/2504.06312/) (2025)
- [Incorporating Inductive Biases to Energy-based Generative Models](https://mlsanity.com/paper/2505.01111/) (2025)
- [GraphBrep: Learning B-Rep in Graph Structure for Efficient CAD Generation](https://mlsanity.com/paper/2507.04765/) (2025)
- [Communication-efficient Federated Graph Classification via Generative Diffusion Modeling](https://mlsanity.com/paper/2601.15722/) (2026)
- [Mitigating topology biases in Graph Diffusion via Counterfactual Intervention](https://mlsanity.com/paper/2603.02005/) (2026)
- [Graph Representation via Elements of Discrete Morse and Cobordism Theories](https://mlsanity.com/paper/2610.01937/) (2026)

## Abstract (arXiv)

Learning to generate graphs is challenging as a graph is a set of pairwise connected, unordered nodes encoding complex combinatorial structures. Recently, several works have proposed graph generative models based on normalizing flows or score-based diffusion models. However, these models need to generate nodes and edges in parallel from the same process, whose dimensionality is unnecessarily high. We propose NVDiff, which takes the VGAE structure and uses a score-based generative model (SGM) as a flexible prior to sample node vectors. By modeling only node vectors in the latent space, NVDiff significantly reduces the dimension of the diffusion process and thus improves sampling speed. Built on the NVDiff framework, we introduce an attention-based score network capable of capturing both local and global contexts of graphs. Experiments indicate that NVDiff significantly reduces computations and can model much larger graphs than competing methods. At the same time, it achieves superior or competitive performances over various datasets compared to previous methods.