# Point-Based Shape Representation Generation with a Correspondence-Preserving Diffusion Model

arXiv: https://arxiv.org/abs/2508.03925 · HTML: https://mlsanity.com/paper/2508.03925/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in 3D, point cloud and scene generation, one of 14 directions in Diffusion models.
- Builds on 14 of its 18 references that are in the map.
- First posted on arXiv 5 Aug 2025.

## Placed in

- Diffusion models / [3D, point cloud and scene generation](https://mlsanity.com/diffusion/3d-point-cloud-and-scene-generation/)

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Attention U-Net: Learning Where to Look for the Pancreas](https://mlsanity.com/paper/1804.03999/) (2018)
- [Diffusion Probabilistic Models for 3D Point Cloud Generation](https://mlsanity.com/paper/2103.01458/) (2021)
- [LION: Latent Point Diffusion Models for 3D Shape Generation](https://mlsanity.com/paper/2210.06978/) (2022)
- [PointFlow: 3D Point Cloud Generation with Continuous Normalizing Flows](https://mlsanity.com/paper/1906.12320/) (2019)
- [Reliable Fidelity and Diversity Metrics for Generative Models](https://mlsanity.com/paper/2002.09797/) (2020)
- [Brain Imaging Generation with Latent Diffusion Models](https://mlsanity.com/paper/2209.07162/) (2022)
- [Medical Diffusion: Denoising Diffusion Probabilistic Models for 3D Medical Image Generation](https://mlsanity.com/paper/2211.03364/) (2022)
- [Diffusion Models for Counterfactual Generation and Anomaly Detection in Brain Images](https://mlsanity.com/paper/2308.02062/) (2023)
- [BiomedJourney: Counterfactual Biomedical Image Generation by Instruction-Learning from Multimodal Patient Journeys](https://mlsanity.com/paper/2310.10765/) (2023)
- [Measuring Feature Dependency of Neural Networks by Collapsing Feature Dimensions in the Data Manifold](https://mlsanity.com/paper/2404.12341/) (2024)
- [Quantifying Hippocampal Shape Asymmetry in Alzheimer's Disease Using Optimal Shape Correspondences](https://mlsanity.com/paper/2312.01043/) (2023)

## Built on by (most cited first, 1 of 1)

- [Deep Spectral Models for Robust Dental Shape Generation](https://mlsanity.com/paper/2606.31293/) (2026)

## Abstract (arXiv)

We propose a diffusion model designed to generate point-based shape representations with correspondences. Traditional statistical shape models have considered point correspondences extensively, but current deep learning methods do not take them into account, focusing on unordered point clouds instead. Current deep generative models for point clouds do not address generating shapes with point correspondences between generated shapes. This work aims to formulate a diffusion model that is capable of generating realistic point-based shape representations, which preserve point correspondences that are present in the training data. Using shape representation data with correspondences derived from Open Access Series of Imaging Studies 3 (OASIS-3), we demonstrate that our correspondence-preserving model effectively generates point-based hippocampal shape representations that are highly realistic compared to existing methods. We further demonstrate the applications of our generative model by downstream tasks, such as conditional generation of healthy and AD subjects and predicting morphological changes of disease progression by counterfactual generation.