# 3D Vessel Graph Generation Using Denoising Diffusion

arXiv: https://arxiv.org/abs/2407.05842 · HTML: https://mlsanity.com/paper/2407.05842/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models.
- Builds on 22 of its 31 references that are in the map.
- First posted on arXiv 8 Jul 2024.

## Placed in

- Diffusion models / [Medical imaging and segmentation](https://mlsanity.com/diffusion/medical-imaging-and-segmentation/)

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

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [A Generalization of Transformer Networks to Graphs](https://mlsanity.com/paper/2012.09699/) (2020)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [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)
- [MiDi: Mixed Graph and 3D Denoising Diffusion for Molecule Generation](https://mlsanity.com/paper/2302.09048/) (2023)
- [Diffusion Models for Graphs Benefit From Discrete State Spaces](https://mlsanity.com/paper/2210.01549/) (2022)
- [MolDiff: Addressing the Atom-Bond Inconsistency Problem in 3D Molecule Diffusion Generation](https://mlsanity.com/paper/2305.07508/) (2023)
- [The TopCoW Challenge -- Topology-Aware Circle of Willis Segmentation for CT and MR Angiography](https://mlsanity.com/paper/2312.17670/) (2023)
- [Graph Denoising Diffusion for Inverse Protein Folding](https://mlsanity.com/paper/2306.16819/) (2023)
- [GraphGDP: Generative Diffusion Processes for Permutation Invariant Graph Generation](https://mlsanity.com/paper/2212.01842/) (2022)
- [MUDiff: Unified Diffusion for Complete Molecule Generation](https://mlsanity.com/paper/2304.14621/) (2023)
- [3D molecule generation by denoising voxel grids](https://mlsanity.com/paper/2306.07473/) (2023)
- [Scalable Robust Graph and Feature Extraction for Arbitrary Vessel Networks in Large Volumetric Datasets](https://mlsanity.com/paper/2102.03444/) (2021)
- [Synthetic optical coherence tomography angiographs for detailed retinal vessel segmentation without human annotations](https://mlsanity.com/paper/2306.10941/) (2023)
- [Blood Vessel Geometry Synthesis using Generative Adversarial Networks](https://mlsanity.com/paper/1804.04381/) (2018)
- [The RETA Benchmark for Retinal Vascular Tree Analysis](https://mlsanity.com/paper/2111.11658/) (2021)
- [VesselVAE: Recursive Variational Autoencoders for 3D Blood Vessel Synthesis](https://mlsanity.com/paper/2307.03592/) (2023)
- [Physiology-based simulation of the retinal vasculature enables annotation-free segmentation of OCT angiographs](https://mlsanity.com/paper/2207.11102/) (2022)
- [Link Prediction for Flow-Driven Spatial Networks](https://mlsanity.com/paper/2303.14501/) (2023)

## Built on by (most cited first, 9 of 9)

- [VesselGPT: Autoregressive Modeling of Vascular Geometry](https://mlsanity.com/paper/2505.13318/) (2025)
- [Hierarchical Part-based Generative Model for Realistic 3D Blood Vessel](https://mlsanity.com/paper/2507.15223/) (2025)
- [Med-Art: Diffusion Transformer for 2D Medical Text-to-Image Generation](https://mlsanity.com/paper/2506.20449/) (2025)
- [Semantically Consistent Discrete Diffusion for 3D Biological Graph Modeling](https://mlsanity.com/paper/2507.04856/) (2025)
- [VesselTok: Tokenizing Vessel-like 3D Biomedical Graph Representations for Reconstruction and Generation](https://mlsanity.com/paper/2603.18797/) (2026)
- [High-Fidelity Medical Shape Generation via Skeletal Latent Diffusion](https://mlsanity.com/paper/2603.07504/) (2026)
- [Sparse Representation Learning for Vessels](https://mlsanity.com/paper/2605.01382/) (2026)
- [Recursive Variational Autoencoders for 3D Blood Vessel Generative Modeling](https://mlsanity.com/paper/2506.14914/) (2025)
- [SynVA: A Modular Toolkit for Vessel Generation and Aneurysm Editing](https://mlsanity.com/paper/2605.17620/) (2026)

## Abstract (arXiv)

Blood vessel networks, represented as 3D graphs, help predict disease biomarkers, simulate blood flow, and aid in synthetic image generation, relevant in both clinical and pre-clinical settings. However, generating realistic vessel graphs that correspond to an anatomy of interest is challenging. Previous methods aimed at generating vessel trees mostly in an autoregressive style and could not be applied to vessel graphs with cycles such as capillaries or specific anatomical structures such as the Circle of Willis. Addressing this gap, we introduce the first application of textitdenoising diffusion models in 3D vessel graph generation. Our contributions include a novel, two-stage generation method that sequentially denoises node coordinates and edges. We experiment with two real-world vessel datasets, consisting of microscopic capillaries and major cerebral vessels, and demonstrate the generalizability of our method for producing diverse, novel, and anatomically plausible vessel graphs.