# SPA-VAE: Similar-Parts-Assignment for Unsupervised 3D Point Cloud Generation

arXiv: https://arxiv.org/abs/2203.07825 · HTML: https://mlsanity.com/paper/2203.07825/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 58 of its 88 references that are in the map.
- First posted on arXiv 15 Mar 2022.

## Builds on (most cited first, 30 of 58)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [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)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Diffusion Probabilistic Models for 3D Point Cloud Generation](https://mlsanity.com/paper/2103.01458/) (2021)
- [3D Shape Generation and Completion through Point-Voxel Diffusion](https://mlsanity.com/paper/2104.03670/) (2021)
- [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)
- [Understanding disentangling in β-VAE](https://mlsanity.com/paper/1804.03599/) (2018)
- [Learning Gradient Fields for Shape Generation](https://mlsanity.com/paper/2008.06520/) (2020)
- [Learning Shape Templates with Structured Implicit Functions](https://mlsanity.com/paper/1904.06447/) (2019)
- [BSP-Net: Generating Compact Meshes via Binary Space Partitioning](https://mlsanity.com/paper/1911.06971/) (2019)
- [Learning Shape Abstractions by Assembling Volumetric Primitives](https://mlsanity.com/paper/1612.00404/) (2016)
- [Unsupervised Learning of Probably Symmetric Deformable 3D Objects from Images in the Wild](https://mlsanity.com/paper/1911.11130/) (2019)
- [CvxNet: Learnable Convex Decomposition](https://mlsanity.com/paper/1909.05736/) (2019)
- [GRNet: Gridding Residual Network for Dense Point Cloud Completion](https://mlsanity.com/paper/2006.03761/) (2020)
- [3D Point Cloud Generative Adversarial Network Based on Tree Structured Graph Convolutions](https://mlsanity.com/paper/1905.06292/) (2019)
- [SnowflakeNet: Point Cloud Completion by Snowflake Point Deconvolution with Skip-Transformer](https://mlsanity.com/paper/2108.04444/) (2021)
- [Modeling Point Clouds with Self-Attention and Gumbel Subset Sampling](https://mlsanity.com/paper/1904.03375/) (2019)
- [Superquadrics Revisited: Learning 3D Shape Parsing beyond Cuboids](https://mlsanity.com/paper/1904.09970/) (2019)
- [Similarity Reasoning and Filtration for Image-Text Matching](https://mlsanity.com/paper/2101.01368/) (2021)
- [Cascaded Refinement Network for Point Cloud Completion](https://mlsanity.com/paper/2004.03327/) (2020)
- [Neural Parts: Learning Expressive 3D Shape Abstractions with Invertible Neural Networks](https://mlsanity.com/paper/2103.10429/) (2021)
- [SoftFlow: Probabilistic Framework for Normalizing Flow on Manifolds](https://mlsanity.com/paper/2006.04604/) (2020)
- [PMP-Net: Point Cloud Completion by Learning Multi-step Point Moving Paths](https://mlsanity.com/paper/2012.03408/) (2020)

## Built on by (most cited first, 2 of 2)

- [FrePolad: Frequency-Rectified Point Latent Diffusion for Point Cloud Generation](https://mlsanity.com/paper/2311.12090/) (2023)
- [Quartet of Diffusions: Structure-Aware Point Cloud Generation through Part and Symmetry Guidance](https://mlsanity.com/paper/2601.20425/) (2026)

## Abstract (arXiv)

This paper addresses the problem of unsupervised parts-aware point cloud generation with learned parts-based self-similarity. Our SPA-VAE infers a set of latent canonical candidate shapes for any given object, along with a set of rigid body transformations for each such candidate shape to one or more locations within the assembled object. In this way, noisy samples on the surface of, say, each leg of a table, are effectively combined to estimate a single leg prototype. When parts-based self-similarity exists in the raw data, sharing data among parts in this way confers numerous advantages: modeling accuracy, appropriately self-similar generative outputs, precise in-filling of occlusions, and model parsimony. SPA-VAE is trained end-to-end using a variational Bayesian approach which uses the Gumbel-softmax trick for the shared part assignments, along with various novel losses to provide appropriate inductive biases. Quantitative and qualitative analyses on ShapeNet demonstrate the advantage of SPA-VAE.