# PU-Flow: a Point Cloud Upsampling Network with Normalizing Flows

arXiv: https://arxiv.org/abs/2107.05893 · HTML: https://mlsanity.com/paper/2107.05893/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 53 of its 80 references that are in the map.
- First posted on arXiv 13 Jul 2021.

## Builds on (most cited first, 30 of 53)

- [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)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [KPConv: Flexible and Deformable Convolution for Point Clouds](https://mlsanity.com/paper/1904.08889/) (2019)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [PointCNN: Convolution On X-Transformed Points](https://mlsanity.com/paper/1801.07791/) (2018)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [Learning Continuous Image Representation with Local Implicit Image Function](https://mlsanity.com/paper/2012.09161/) (2020)
- [Revisiting Point Cloud Classification: A New Benchmark Dataset and Classification Model on Real-World Data](https://mlsanity.com/paper/1908.04616/) (2019)
- [PointFlow: 3D Point Cloud Generation with Continuous Normalizing Flows](https://mlsanity.com/paper/1906.12320/) (2019)
- [PCN: Point Completion Network](https://mlsanity.com/paper/1808.00671/) (2018)
- [StyleFlow: Attribute-conditioned Exploration of StyleGAN-Generated Images using Conditional Continuous Normalizing Flows](https://mlsanity.com/paper/2008.02401/) (2020)
- [Relation-Shape Convolutional Neural Network for Point Cloud Analysis](https://mlsanity.com/paper/1904.07601/) (2019)
- [WaveGlow: A Flow-based Generative Network for Speech Synthesis](https://mlsanity.com/paper/1811.00002/) (2018)
- [PointNetLK: Robust & Efficient Point Cloud Registration using PointNet](https://mlsanity.com/paper/1903.05711/) (2019)
- [PAConv: Position Adaptive Convolution with Dynamic Kernel Assembling on Point Clouds](https://mlsanity.com/paper/2103.14635/) (2021)
- [SO-Net: Self-Organizing Network for Point Cloud Analysis](https://mlsanity.com/paper/1803.04249/) (2018)
- [PU-Net: Point Cloud Upsampling Network](https://mlsanity.com/paper/1801.06761/) (2018)
- [SRFlow: Learning the Super-Resolution Space with Normalizing Flow](https://mlsanity.com/paper/2006.14200/) (2020)
- [Thingi10K: A Dataset of 10,000 3D-Printing Models](https://mlsanity.com/paper/1605.04797/) (2016)
- [Meta-SR: A Magnification-Arbitrary Network for Super-Resolution](https://mlsanity.com/paper/1903.00875/) (2019)
- [Learning Likelihoods with Conditional Normalizing Flows](https://mlsanity.com/paper/1912.00042/) (2019)

## Built on by (most cited first, 17 of 17)

- [GaussianHead: High-fidelity Head Avatars with Learnable Gaussian Derivation](https://mlsanity.com/paper/2312.01632/) (2023)
- [GeoUDF: Surface Reconstruction from 3D Point Clouds via Geometry-guided Distance Representation](https://mlsanity.com/paper/2211.16762/) (2022)
- [DMF-Net: Image-Guided Point Cloud Completion with Dual-Channel Modality Fusion and Shape-Aware Upsampling Transformer](https://mlsanity.com/paper/2406.17319/) (2024)
- [iPUNet:Iterative Cross Field Guided Point Cloud Upsampling](https://mlsanity.com/paper/2310.09092/) (2023)
- [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)
- [CS-Net:Contribution-based Sampling Network for Point Cloud Simplification](https://mlsanity.com/paper/2501.10789/) (2025)
- [Rethinking Data Input for Point Cloud Upsampling](https://mlsanity.com/paper/2407.04476/) (2024)
- [Generative Unordered Flow for Set-Structured Data Generation](https://mlsanity.com/paper/2501.17770/) (2025)
- [SuperCarver: Texture-Consistent 3D Geometry Super-Resolution for High-Fidelity Surface Detail Generation](https://mlsanity.com/paper/2503.09439/) (2025)
- [MBPU: A Plug-and-Play State Space Model for Point Cloud Upsamping with Fast Point Rendering](https://mlsanity.com/paper/2410.15941/) (2024)
- [SPU-IMR: Self-supervised Arbitrary-scale Point Cloud Upsampling via Iterative Mask-recovery Network](https://mlsanity.com/paper/2502.19452/) (2025)
- [Deep Learning based Joint Geometry and Attribute Up-sampling for Large-Scale Colored Point Clouds](https://mlsanity.com/paper/2506.22749/) (2025)
- [Point upsampling networks for single-photon sensing](https://mlsanity.com/paper/2508.12986/) (2025)
- [PVNet: Point-Voxel Interaction LiDAR Scene Upsampling Via Diffusion Models](https://mlsanity.com/paper/2508.17050/) (2025)
- [PUFM++: Point Cloud Upsampling via Enhanced Flow Matching](https://mlsanity.com/paper/2512.20988/) (2025)
- [PLSR: Progressive and Localized Super-Resolution of 3D Objects via Localized Latent Voxel Diffusion](https://mlsanity.com/paper/2609.06436/) (2026)

## Abstract (arXiv)

Point cloud upsampling aims to generate dense point clouds from given sparse ones, which is a challenging task due to the irregular and unordered nature of point sets. To address this issue, we present a novel deep learning-based model, called PU-Flow, which incorporates normalizing flows and weight prediction techniques to produce dense points uniformly distributed on the underlying surface. Specifically, we exploit the invertible characteristics of normalizing flows to transform points between Euclidean and latent spaces and formulate the upsampling process as ensemble of neighbouring points in a latent space, where the ensemble weights are adaptively learned from local geometric context. Extensive experiments show that our method is competitive and, in most test cases, it outperforms state-of-the-art methods in terms of reconstruction quality, proximity-to-surface accuracy, and computation efficiency. The source code will be publicly available at https://github.com/unknownue/pu-flow.