# PCRDiffusion: Diffusion Probabilistic Models for Point Cloud Registration

arXiv: https://arxiv.org/abs/2312.06063 · HTML: https://mlsanity.com/paper/2312.06063/

## Key facts

- Cited by 3 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 47 of its 72 references that are in the map.
- First posted on arXiv 11 Dec 2023.

## 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, 30 of 47)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Blended Diffusion for Text-driven Editing of Natural Images](https://mlsanity.com/paper/2111.14818/) (2021)
- [Diffusion Probabilistic Models for 3D Point Cloud Generation](https://mlsanity.com/paper/2103.01458/) (2021)
- [Open3D: A Modern Library for 3D Data Processing](https://mlsanity.com/paper/1801.09847/) (2018)
- [NICE-SLAM: Neural Implicit Scalable Encoding for SLAM](https://mlsanity.com/paper/2112.12130/) (2021)
- [LION: Latent Point Diffusion Models for 3D Shape Generation](https://mlsanity.com/paper/2210.06978/) (2022)
- [3D Shape Generation and Completion through Point-Voxel Diffusion](https://mlsanity.com/paper/2104.03670/) (2021)
- [Label-Efficient Semantic Segmentation with Diffusion Models](https://mlsanity.com/paper/2112.03126/) (2021)
- [DiffusionDet: Diffusion Model for Object Detection](https://mlsanity.com/paper/2211.09788/) (2022)
- [3DMatch: Learning Local Geometric Descriptors from RGB-D Reconstructions](https://mlsanity.com/paper/1603.08182/) (2016)
- [Deep Closest Point: Learning Representations for Point Cloud Registration](https://mlsanity.com/paper/1905.03304/) (2019)
- [PREDATOR: Registration of 3D Point Clouds with Low Overlap](https://mlsanity.com/paper/2011.13005/) (2020)
- [SegDiff: Image Segmentation with Diffusion Probabilistic Models](https://mlsanity.com/paper/2112.00390/) (2021)
- [PointNetLK: Robust & Efficient Point Cloud Registration using PointNet](https://mlsanity.com/paper/1903.05711/) (2019)
- [Diffusion models as plug-and-play priors](https://mlsanity.com/paper/2206.09012/) (2022)
- [Deep Global Registration](https://mlsanity.com/paper/2004.11540/) (2020)
- [Diffusion Models for Implicit Image Segmentation Ensembles](https://mlsanity.com/paper/2112.03145/) (2021)
- [RPM-Net: Robust Point Matching using Learned Features](https://mlsanity.com/paper/2003.13479/) (2020)

## Built on by (most cited first, 3 of 3)

- [CHAMP: Conformalized 3D Human Multi-Hypothesis Pose Estimators](https://mlsanity.com/paper/2407.06141/) (2024)
- [Equivariant Flow Matching for Point Cloud Assembly](https://mlsanity.com/paper/2505.21539/) (2025)
- [Joint Localization and Planning using Diffusion](https://mlsanity.com/paper/2409.17995/) (2024)

## Abstract (arXiv)

We propose a new framework that formulates point cloud registration as a denoising diffusion process from noisy transformation to object transformation. During training stage, object transformation diffuses from ground-truth transformation to random distribution, and the model learns to reverse this noising process. In sampling stage, the model refines randomly generated transformation to the output result in a progressive way. We derive the variational bound in closed form for training and provide implementations of the model. Our work provides the following crucial findings: (i) In contrast to most existing methods, our framework, Diffusion Probabilistic Models for Point Cloud Registration (PCRDiffusion) does not require repeatedly update source point cloud to refine the predicted transformation. (ii) Point cloud registration, one of the representative discriminative tasks, can be solved by a generative way and the unified probabilistic formulation. Finally, we discuss and provide an outlook on the application of diffusion model in different scenarios for point cloud registration. Experimental results demonstrate that our model achieves competitive performance in point cloud registration. In correspondence-free and correspondence-based scenarios, PCRDifussion can both achieve exceeding 50% performance improvements.