# TrIND: Representing Anatomical Trees by Denoising Diffusion of Implicit Neural Fields

arXiv: https://arxiv.org/abs/2403.08974 · HTML: https://mlsanity.com/paper/2403.08974/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models.
- Builds on 17 of its 42 references that are in the map.
- First posted on arXiv 13 Mar 2024.

## Placed in

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

## Builds on (most cited first, 17 of 17)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Differentiable Volumetric Rendering: Learning Implicit 3D Representations without 3D Supervision](https://mlsanity.com/paper/1912.07372/) (2019)
- [3DShape2VecSet: A 3D Shape Representation for Neural Fields and Generative Diffusion Models](https://mlsanity.com/paper/2301.11445/) (2023)
- [Volumetric and Multi-View CNNs for Object Classification on 3D Data](https://mlsanity.com/paper/1604.03265/) (2016)
- [HyperDiffusion: Generating Implicit Neural Fields with Weight-Space Diffusion](https://mlsanity.com/paper/2303.17015/) (2023)
- [Diffusion-SDF: Conditional Generative Modeling of Signed Distance Functions](https://mlsanity.com/paper/2211.13757/) (2022)
- [Learning to Learn with Generative Models of Neural Network Checkpoints](https://mlsanity.com/paper/2209.12892/) (2022)
- [Subdivision-Based Mesh Convolution Networks](https://mlsanity.com/paper/2106.02285/) (2021)
- [IntrA: 3D Intracranial Aneurysm Dataset for Deep Learning](https://mlsanity.com/paper/2003.02920/) (2020)
- [Going Off-Grid: Continuous Implicit Neural Representations for 3D Vascular Modeling](https://mlsanity.com/paper/2207.14663/) (2022)
- [Blood Vessel Geometry Synthesis using Generative Adversarial Networks](https://mlsanity.com/paper/1804.04381/) (2018)
- [VesselVAE: Recursive Variational Autoencoders for 3D Blood Vessel Synthesis](https://mlsanity.com/paper/2307.03592/) (2023)

## Built on by (most cited first, 4 of 4)

- [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)
- [High-Fidelity Medical Shape Generation via Skeletal Latent Diffusion](https://mlsanity.com/paper/2603.07504/) (2026)
- [Recursive Variational Autoencoders for 3D Blood Vessel Generative Modeling](https://mlsanity.com/paper/2506.14914/) (2025)

## Abstract (arXiv)

Anatomical trees play a central role in clinical diagnosis and treatment planning. However, accurately representing anatomical trees is challenging due to their varying and complex topology and geometry. Traditional methods for representing tree structures, captured using medical imaging, while invaluable for visualizing vascular and bronchial networks, exhibit drawbacks in terms of limited resolution, flexibility, and efficiency. Recently, implicit neural representations (INRs) have emerged as a powerful tool for representing shapes accurately and efficiently. We propose a novel approach, TrIND, for representing anatomical trees using INR, while also capturing the distribution of a set of trees via denoising diffusion in the space of INRs. We accurately capture the intricate geometries and topologies of anatomical trees at any desired resolution. Through extensive qualitative and quantitative evaluation, we demonstrate high-fidelity tree reconstruction with arbitrary resolution yet compact storage, and versatility across anatomical sites and tree complexities. The code is available at: texttturlhttps://github.com/sinashish/TreeDiffusion.