# GenSP: Consistent Spherical Parameterization via Learning Shape Generative Models

arXiv: https://arxiv.org/abs/2607.00492 · HTML: https://mlsanity.com/paper/2607.00492/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 33 of its 70 references that are in the map.
- First posted on arXiv 1 Jul 2026.

## Builds on (most cited first, 30 of 33)

- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [D-NeRF: Neural Radiance Fields for Dynamic Scenes](https://mlsanity.com/paper/2011.13961/) (2020)
- [Non-Rigid Neural Radiance Fields: Reconstruction and Novel View Synthesis of a Dynamic Scene From Monocular Video](https://mlsanity.com/paper/2012.12247/) (2020)
- [Implicit Functions in Feature Space for 3D Shape Reconstruction and Completion](https://mlsanity.com/paper/2003.01456/) (2020)
- [3D Menagerie: Modeling the 3D shape and pose of animals](https://mlsanity.com/paper/1611.07700/) (2016)
- [Generating 3D faces using Convolutional Mesh Autoencoders](https://mlsanity.com/paper/1807.10267/) (2018)
- [3D-CODED : 3D Correspondences by Deep Deformation](https://mlsanity.com/paper/1806.05228/) (2018)
- [Deep Functional Maps: Structured Prediction for Dense Shape Correspondence](https://mlsanity.com/paper/1704.08686/) (2017)
- [Deep Geometric Functional Maps: Robust Feature Learning for Shape Correspondence](https://mlsanity.com/paper/2003.14286/) (2020)
- [SALD: Sign Agnostic Learning with Derivatives](https://mlsanity.com/paper/2006.05400/) (2020)
- [Neural 3D Morphable Models: Spiral Convolutional Networks for 3D Shape Representation Learning and Generation](https://mlsanity.com/paper/1905.02876/) (2019)
- [NeuroMorph: Unsupervised Shape Interpolation and Correspondence in One Go](https://mlsanity.com/paper/2106.09431/) (2021)
- [Unsupervised Shape and Pose Disentanglement for 3D Meshes](https://mlsanity.com/paper/2007.11341/) (2020)
- [DPFM: Deep Partial Functional Maps](https://mlsanity.com/paper/2110.09994/) (2021)
- [Unsupervised Learning of Robust Spectral Shape Matching](https://mlsanity.com/paper/2304.14419/) (2023)
- [LIMP: Learning Latent Shape Representations with Metric Preservation Priors](https://mlsanity.com/paper/2003.12283/) (2020)
- [Diffusion 3D Features (Diff3F): Decorating Untextured Shapes with Distilled Semantic Features](https://mlsanity.com/paper/2311.17024/) (2023)
- [Fully Convolutional Mesh Autoencoder using Efficient Spatially Varying Kernels](https://mlsanity.com/paper/2006.04325/) (2020)
- [KeypointNet: A Large-scale 3D Keypoint Dataset Aggregated from Numerous Human Annotations](https://mlsanity.com/paper/2002.12687/) (2020)
- [Shape registration in the time of transformers](https://mlsanity.com/paper/2106.13679/) (2021)
- [ARAPReg: An As-Rigid-As Possible Regularization Loss for Learning Deformable Shape Generators](https://mlsanity.com/paper/2108.09432/) (2021)
- [Deep Orientation-Aware Functional Maps: Tackling Symmetry Issues in Shape Matching](https://mlsanity.com/paper/2204.13453/) (2022)
- [Multi-Image Matching via Fast Alternating Minimization](https://mlsanity.com/paper/1505.04845/) (2015)
- [Augmenting Implicit Neural Shape Representations with Explicit Deformation Fields](https://mlsanity.com/paper/2108.08931/) (2021)
- [Neural Geometry Processing via Spherical Neural Surfaces](https://mlsanity.com/paper/2407.07755/) (2024)
- [Denoising Functional Maps: Diffusion Models for Shape Correspondence](https://mlsanity.com/paper/2503.01845/) (2025)
- [GenCorres: Consistent Shape Matching via Coupled Implicit-Explicit Shape Generative Models](https://mlsanity.com/paper/2304.10523/) (2023)
- [Deformation Recovery: Localized Learning for Detail-Preserving Deformations](https://mlsanity.com/paper/2410.08225/) (2024)
- [DiffuMatch: Category-Agnostic Spectral Diffusion Priors for Robust Non-rigid Shape Matching](https://mlsanity.com/paper/2507.23715/) (2025)

## Abstract (arXiv)

We introduce GenSP, a data-driven framework that learns consistent spherical parameterizations across a collection of genus-0 shapes. Instead of optimizing the parameterization of each shape independently, our method learns a neural generative model that predicts a continuous mapping from the unit sphere to shapes in a dataset. Under this formulation, spherical parameterizations are obtained through the inverse mappings of the learned generator, which encourages similar shapes to share consistent parameterizations. To make this formulation practical, we address several key challenges in learning such a generative model. First, we introduce a continuous neural deformation model that predicts surface points from sphere coordinates and latent shape codes, avoiding discretization artifacts common in mesh-based formulations. Second, we augment the training space with intermediate shapes that bridge the sphere and input shapes, allowing the model to learn meaningful deformations across a heterogeneous shape collection. Third, we compute reliable initial correspondences by propagating mappings along a spanning tree of training shapes in the latent space. Experiments on the ShapeNet dataset demonstrate that our approach significantly reduces geometric distortion and improves cross-shape consistency compared with state-of-the-art spherical parameterization methods.