# Semantically Consistent Discrete Diffusion for 3D Biological Graph Modeling

arXiv: https://arxiv.org/abs/2507.04856 · HTML: https://mlsanity.com/paper/2507.04856/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models.
- Builds on 14 of its 27 references that are in the map.
- First posted on arXiv 7 Jul 2025.

## Placed in

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

## Builds on (most cited first, 14 of 14)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution](https://mlsanity.com/paper/2310.16834/) (2023)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [Protein Design with Guided Discrete Diffusion](https://mlsanity.com/paper/2305.20009/) (2023)
- [MiDi: Mixed Graph and 3D Denoising Diffusion for Molecule Generation](https://mlsanity.com/paper/2302.09048/) (2023)
- [The TopCoW Challenge -- Topology-Aware Circle of Willis Segmentation for CT and MR Angiography](https://mlsanity.com/paper/2312.17670/) (2023)
- [Generative Modelling of Structurally Constrained Graphs](https://mlsanity.com/paper/2406.17341/) (2024)
- [vesselFM: A Foundation Model for Universal 3D Blood Vessel Segmentation](https://mlsanity.com/paper/2411.17386/) (2024)
- [Scalable Robust Graph and Feature Extraction for Arbitrary Vessel Networks in Large Volumetric Datasets](https://mlsanity.com/paper/2102.03444/) (2021)
- [VesselVAE: Recursive Variational Autoencoders for 3D Blood Vessel Synthesis](https://mlsanity.com/paper/2307.03592/) (2023)
- [3D Vessel Graph Generation Using Denoising Diffusion](https://mlsanity.com/paper/2407.05842/) (2024)
- [MorphGrower: A Synchronized Layer-by-layer Growing Approach for Plausible Neuronal Morphology Generation](https://mlsanity.com/paper/2401.09500/) (2024)
- [Rigorous mathematical optimization of synthetic hepatic vascular trees](https://mlsanity.com/paper/2202.04406/) (2022)

## Built on by (most cited first, 2 of 2)

- [VesselTok: Tokenizing Vessel-like 3D Biomedical Graph Representations for Reconstruction and Generation](https://mlsanity.com/paper/2603.18797/) (2026)
- [Sparse Representation Learning for Vessels](https://mlsanity.com/paper/2605.01382/) (2026)

## Abstract (arXiv)

3D spatial graphs play a crucial role in biological and clinical research by modeling anatomical networks such as blood vessels,neurons, and airways. However, generating 3D biological graphs while maintaining anatomical validity remains challenging, a key limitation of existing diffusion-based methods. In this work, we propose a novel 3D biological graph generation method that adheres to structural and semantic plausibility conditions. We achieve this by using a novel projection operator during sampling that stochastically fixes inconsistencies. Further, we adopt a superior edge-deletion-based noising procedure suitable for sparse biological graphs. Our method demonstrates superior performance on two real-world datasets, human circle of Willis and lung airways, compared to previous approaches. Importantly, we demonstrate that the generated samples significantly enhance downstream graph labeling performance. Furthermore, we show that our generative model is a reasonable out-of-the-box link predictior.