# Grad-PU: Arbitrary-Scale Point Cloud Upsampling via Gradient Descent with Learned Distance Functions

arXiv: https://arxiv.org/abs/2304.11846 · HTML: https://mlsanity.com/paper/2304.11846/

## Key facts

- Cited by 43 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 50 references that are in the map.
- First posted on arXiv 24 Apr 2023.

## Builds on (most cited first, 30 of 42)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [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)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Point Transformer](https://mlsanity.com/paper/2011.00931/) (2020)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [PoseCNN: A Convolutional Neural Network for 6D Object Pose Estimation in Cluttered Scenes](https://mlsanity.com/paper/1711.00199/) (2017)
- [PointCNN: Convolution On X-Transformed Points](https://mlsanity.com/paper/1801.07791/) (2018)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [PointConv: Deep Convolutional Networks on 3D Point Clouds](https://mlsanity.com/paper/1811.07246/) (2018)
- [Deep Learning for 3D Point Clouds: A Survey](https://mlsanity.com/paper/1912.12033/) (2019)
- [Revisiting Point Cloud Classification: A New Benchmark Dataset and Classification Model on Real-World Data](https://mlsanity.com/paper/1908.04616/) (2019)
- [Local Implicit Grid Representations for 3D Scenes](https://mlsanity.com/paper/2003.08981/) (2020)
- [Implicit Functions in Feature Space for 3D Shape Reconstruction and Completion](https://mlsanity.com/paper/2003.01456/) (2020)
- [OctNet: Learning Deep 3D Representations at High Resolutions](https://mlsanity.com/paper/1611.05009/) (2016)
- [Neural Unsigned Distance Fields for Implicit Function Learning](https://mlsanity.com/paper/2010.13938/) (2020)
- [PU-Net: Point Cloud Upsampling Network](https://mlsanity.com/paper/1801.06761/) (2018)
- [Walk in the Cloud: Learning Curves for Point Clouds Shape Analysis](https://mlsanity.com/paper/2105.01288/) (2021)
- [PU-GAN: a Point Cloud Upsampling Adversarial Network](https://mlsanity.com/paper/1907.10844/) (2019)
- [Patch-based Progressive 3D Point Set Upsampling](https://mlsanity.com/paper/1811.11286/) (2018)
- [PU-GCN: Point Cloud Upsampling using Graph Convolutional Networks](https://mlsanity.com/paper/1912.03264/) (2019)
- [EC-Net: an Edge-aware Point set Consolidation Network](https://mlsanity.com/paper/1807.06010/) (2018)
- [Score-Based Point Cloud Denoising](https://mlsanity.com/paper/2107.10981/) (2021)
- [Point Cloud Upsampling via Disentangled Refinement](https://mlsanity.com/paper/2106.04779/) (2021)

## Built on by (most cited first, 30 of 43)

- [RangeLDM: Fast Realistic LiDAR Point Cloud Generation](https://mlsanity.com/paper/2403.10094/) (2024)
- [A Conditional Denoising Diffusion Probabilistic Model for Point Cloud Upsampling](https://mlsanity.com/paper/2312.02719/) (2023)
- [Advancements in Point Cloud Data Augmentation for Deep Learning: A Survey](https://mlsanity.com/paper/2308.12113/) (2023)
- [An End-to-End Robust Point Cloud Semantic Segmentation Network with Single-Step Conditional Diffusion Models](https://mlsanity.com/paper/2411.16308/) (2024)
- [CRA-PCN: Point Cloud Completion with Intra- and Inter-level Cross-Resolution Transformers](https://mlsanity.com/paper/2401.01552/) (2024)
- [SAGS: Structure-Aware 3D Gaussian Splatting](https://mlsanity.com/paper/2404.19149/) (2024)
- [SuperPC: A Single Diffusion Model for Point Cloud Completion, Upsampling, Denoising, and Colorization](https://mlsanity.com/paper/2503.14558/) (2025)
- [Learning Continuous Implicit Field with Local Distance Indicator for Arbitrary-Scale Point Cloud Upsampling](https://mlsanity.com/paper/2312.15133/) (2023)
- [FrePolad: Frequency-Rectified Point Latent Diffusion for Point Cloud Generation](https://mlsanity.com/paper/2311.12090/) (2023)
- [PointNSP: Autoregressive 3D Point Cloud Generation with Next-Scale Level-of-Detail Prediction](https://mlsanity.com/paper/2510.05613/) (2025)
- [Arbitrary-Scale Point Cloud Upsampling by Voxel-Based Network with Latent Geometric-Consistent Learning](https://mlsanity.com/paper/2403.05117/) (2024)
- [Fast Point Cloud Geometry Compression with Context-based Residual Coding and INR-based Refinement](https://mlsanity.com/paper/2408.02966/) (2024)
- [Deep Learning for 3D Point Cloud Enhancement: A Survey](https://mlsanity.com/paper/2411.00857/) (2024)
- [Efficient Point Clouds Upsampling via Flow Matching](https://mlsanity.com/paper/2501.15286/) (2025)
- [Fourier Decomposition for Explicit Representation of 3D Point Cloud Attributes](https://mlsanity.com/paper/2503.10055/) (2025)
- [A Self-Conditioned Representation Guided Diffusion Model for Realistic Text-to-LiDAR Scene Generation](https://mlsanity.com/paper/2511.19004/) (2025)
- [Image-Guided Outdoor LiDAR Perception Quality Assessment for Autonomous Driving](https://mlsanity.com/paper/2406.17265/) (2024)
- [Joint Point Cloud Upsampling and Cleaning with Octree-based CNNs](https://mlsanity.com/paper/2410.17001/) (2024)
- [LangDriveCTRL: Natural Language Controllable Driving Scene Editing with Multi-modal Agents](https://mlsanity.com/paper/2512.17445/) (2025)
- [Rethinking Data Input for Point Cloud Upsampling](https://mlsanity.com/paper/2407.04476/) (2024)
- [Point Cloud Resampling with Learnable Heat Diffusion](https://mlsanity.com/paper/2411.14120/) (2024)
- [SceneOrchestra: Efficient Agentic 3D Scene Synthesis via Full Tool-Call Trajectory Generation](https://mlsanity.com/paper/2604.19907/) (2026)
- [PU-Ray: Domain-Independent Point Cloud Upsampling via Ray Marching on Neural Implicit Surface](https://mlsanity.com/paper/2310.08755/) (2023)
- [GaussianPU: A Hybrid 2D-3D Upsampling Framework for Enhancing Color Point Clouds via 3D Gaussian Splatting](https://mlsanity.com/paper/2409.01581/) (2024)
- [MBPU: A Plug-and-Play State Space Model for Point Cloud Upsamping with Fast Point Rendering](https://mlsanity.com/paper/2410.15941/) (2024)
- [Att2CPC: Attention-Guided Lossy Attribute Compression of Point Clouds](https://mlsanity.com/paper/2410.17823/) (2024)
- [PLATYPUS: Progressive Local Surface Estimator for Arbitrary-Scale Point Cloud Upsampling](https://mlsanity.com/paper/2411.00432/) (2024)
- [Representation Learning of Point Cloud Upsampling in Global and Local Inputs](https://mlsanity.com/paper/2501.07076/) (2025)
- [VoLUT: Efficient Volumetric streaming enhanced by LUT-based super-resolution](https://mlsanity.com/paper/2502.12151/) (2025)
- [SPU-IMR: Self-supervised Arbitrary-scale Point Cloud Upsampling via Iterative Mask-recovery Network](https://mlsanity.com/paper/2502.19452/) (2025)

## Abstract (arXiv)

Most existing point cloud upsampling methods have roughly three steps: feature extraction, feature expansion and 3D coordinate prediction. However,they usually suffer from two critical issues: (1)fixed upsampling rate after one-time training, since the feature expansion unit is customized for each upsampling rate; (2)outliers or shrinkage artifact caused by the difficulty of precisely predicting 3D coordinates or residuals of upsampled points. To adress them, we propose a new framework for accurate point cloud upsampling that supports arbitrary upsampling rates. Our method first interpolates the low-res point cloud according to a given upsampling rate. And then refine the positions of the interpolated points with an iterative optimization process, guided by a trained model estimating the difference between the current point cloud and the high-res target. Extensive quantitative and qualitative results on benchmarks and downstream tasks demonstrate that our method achieves the state-of-the-art accuracy and efficiency.