# Point Cloud Denoising via Momentum Ascent in Gradient Fields

arXiv: https://arxiv.org/abs/2202.10094 · HTML: https://mlsanity.com/paper/2202.10094/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 22 references that are in the map.
- First posted on arXiv 21 Feb 2022.

## Builds on (most cited first, 11 of 11)

- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [Accelerating 3D Deep Learning with PyTorch3D](https://mlsanity.com/paper/2007.08501/) (2020)
- [PU-Net: Point Cloud Upsampling Network](https://mlsanity.com/paper/1801.06761/) (2018)
- [PointCleanNet: Learning to Denoise and Remove Outliers from Dense Point Clouds](https://mlsanity.com/paper/1901.01060/) (2019)
- [Score-Based Point Cloud Denoising](https://mlsanity.com/paper/2107.10981/) (2021)
- [Total Denoising: Unsupervised Learning of 3D Point Cloud Cleaning](https://mlsanity.com/paper/1904.07615/) (2019)
- [Differentiable Manifold Reconstruction for Point Cloud Denoising](https://mlsanity.com/paper/2007.13551/) (2020)
- [3D Point Cloud Denoising using Graph Laplacian Regularization of a Low Dimensional Manifold Model](https://mlsanity.com/paper/1803.07252/) (2018)
- [Learning Graph-Convolutional Representations for Point Cloud Denoising](https://mlsanity.com/paper/2007.02578/) (2020)
- [3D Point Cloud Denoising via Deep Neural Network based Local Surface Estimation](https://mlsanity.com/paper/1904.04427/) (2019)
- [MANet: Improving Video Denoising with a Multi-Alignment Network](https://mlsanity.com/paper/2202.09704/) (2022)

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

- [P2P-Bridge: Diffusion Bridges for 3D Point Cloud Denoising](https://mlsanity.com/paper/2408.16325/) (2024)
- [Deep Learning For Point Cloud Denoising: A Survey](https://mlsanity.com/paper/2508.11932/) (2025)
- [Incomplete Gamma Kernels: Generalizing Locally Optimal Projection Operators](https://mlsanity.com/paper/2205.01087/) (2022)
- [A Survey of Deep Learning-based Point Cloud Denoising](https://mlsanity.com/paper/2508.17011/) (2025)

## Abstract (arXiv)

To achieve point cloud denoising, traditional methods heavily rely on geometric priors, and most learning-based approaches suffer from outliers and loss of details. Recently, the gradient-based method was proposed to estimate the gradient fields from the noisy point clouds using neural networks, and refine the position of each point according to the estimated gradient. However, the predicted gradient could fluctuate, leading to perturbed and unstable solutions, as well as a long inference time. To address these issues, we develop the momentum gradient ascent method that leverages the information of previous iterations in determining the trajectories of the points, thus improving the stability of the solution and reducing the inference time. Experiments demonstrate that the proposed method outperforms state-of-the-art approaches with a variety of point clouds, noise types, and noise levels. Code is available at: https://github.com/IndigoPurple/MAG