# Go with the Flows: Mixtures of Normalizing Flows for Point Cloud Generation and Reconstruction

arXiv: https://arxiv.org/abs/2106.03135 · HTML: https://mlsanity.com/paper/2106.03135/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 59 references that are in the map.
- First posted on arXiv 6 Jun 2021.

## Builds on (most cited first, 30 of 43)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [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)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [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)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [Diffusion Probabilistic Models for 3D Point Cloud Generation](https://mlsanity.com/paper/2103.01458/) (2021)
- [Pixel2Mesh: Generating 3D Mesh Models from Single RGB Images](https://mlsanity.com/paper/1804.01654/) (2018)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [3D-R2N2: A Unified Approach for Single and Multi-view 3D Object Reconstruction](https://mlsanity.com/paper/1604.00449/) (2016)
- [Deep Learning for 3D Point Clouds: A Survey](https://mlsanity.com/paper/1912.12033/) (2019)
- [AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generation](https://mlsanity.com/paper/1802.05384/) (2018)
- [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)
- [What Do Single-view 3D Reconstruction Networks Learn?](https://mlsanity.com/paper/1905.03678/) (2019)
- [Learning Gradient Fields for Shape Generation](https://mlsanity.com/paper/2008.06520/) (2020)
- [SRFlow: Learning the Super-Resolution Space with Normalizing Flow](https://mlsanity.com/paper/2006.14200/) (2020)
- [Variational Lossy Autoencoder](https://mlsanity.com/paper/1611.02731/) (2016)
- [3D Point Cloud Generative Adversarial Network Based on Tree Structured Graph Convolutions](https://mlsanity.com/paper/1905.06292/) (2019)
- [Guided Image Generation with Conditional Invertible Neural Networks](https://mlsanity.com/paper/1907.02392/) (2019)
- [Flows for simultaneous manifold learning and density estimation](https://mlsanity.com/paper/2003.13913/) (2020)
- [PointGrow: Autoregressively Learned Point Cloud Generation with Self-Attention](https://mlsanity.com/paper/1810.05591/) (2018)
- [Neural Parts: Learning Expressive 3D Shape Abstractions with Invertible Neural Networks](https://mlsanity.com/paper/2103.10429/) (2021)

## Built on by (most cited first, 16 of 16)

- [SDF-StyleGAN: Implicit SDF-Based StyleGAN for 3D Shape Generation](https://mlsanity.com/paper/2206.12055/) (2022)
- [Sketch and Text Guided Diffusion Model for Colored Point Cloud Generation](https://mlsanity.com/paper/2308.02874/) (2023)
- [GECCO: Geometrically-Conditioned Point Diffusion Models](https://mlsanity.com/paper/2303.05916/) (2023)
- [PD-Flow: A Point Cloud Denoising Framework with Normalizing Flows](https://mlsanity.com/paper/2203.05940/) (2022)
- [PU-Flow: a Point Cloud Upsampling Network with Normalizing Flows](https://mlsanity.com/paper/2107.05893/) (2021)
- [PSRFlow: Probabilistic Super Resolution with Flow-Based Models for Scientific Data](https://mlsanity.com/paper/2308.04605/) (2023)
- [Topology-Matching Normalizing Flows for Out-of-Distribution Detection in Robot Learning](https://mlsanity.com/paper/2311.06481/) (2023)
- [Flow-based GAN for 3D Point Cloud Generation from a Single Image](https://mlsanity.com/paper/2210.04072/) (2022)
- [Point Cloud Part Editing: Segmentation, Generation, Assembly, and Selection](https://mlsanity.com/paper/2312.11867/) (2023)
- [FFHFlow: Diverse and Uncertainty-Aware Dexterous Grasp Generation via Flow Variational Inference](https://mlsanity.com/paper/2407.15161/) (2024)
- [SPA-VAE: Similar-Parts-Assignment for Unsupervised 3D Point Cloud Generation](https://mlsanity.com/paper/2203.07825/) (2022)
- [ManiFlow: Implicitly Representing Manifolds with Normalizing Flows](https://mlsanity.com/paper/2208.08932/) (2022)
- [Diverse Shape Completion via Style Modulated Generative Adversarial Networks](https://mlsanity.com/paper/2311.11184/) (2023)
- [Marginalization Consistent Probabilistic Forecasting of Irregular Time Series via Mixture of Separable flows](https://mlsanity.com/paper/2406.07246/) (2024)
- [Classifier Weighted Mixture models](https://mlsanity.com/paper/2501.02989/) (2025)
- [NF-SLAM: Effective, Normalizing Flow-supported Neural Field representations for object-level visual SLAM in automotive applications](https://mlsanity.com/paper/2503.11199/) (2025)

## Abstract (arXiv)

Recently normalizing flows (NFs) have demonstrated state-of-the-art performance on modeling 3D point clouds while allowing sampling with arbitrary resolution at inference time. However, these flow-based models still require long training times and large models for representing complicated geometries. This work enhances their representational power by applying mixtures of NFs to point clouds. We show that in this more general framework each component learns to specialize in a particular subregion of an object in a completely unsupervised fashion. By instantiating each mixture component with a comparatively small NF we generate point clouds with improved details compared to single-flow-based models while using fewer parameters and considerably reducing the inference runtime. We further demonstrate that by adding data augmentation, individual mixture components can learn to specialize in a semantically meaningful manner. We evaluate mixtures of NFs on generation, autoencoding and single-view reconstruction based on the ShapeNet dataset.