# Explorable Mesh Deformation Subspaces from Unstructured Generative Models

arXiv: https://arxiv.org/abs/2310.07814 · HTML: https://mlsanity.com/paper/2310.07814/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 59 references that are in the map.
- First posted on arXiv 11 Oct 2023.

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

- [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)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [FaceNet: A Unified Embedding for Face Recognition and Clustering](https://mlsanity.com/paper/1503.03832/) (2015)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Pixel2Mesh: Generating 3D Mesh Models from Single RGB Images](https://mlsanity.com/paper/1804.01654/) (2018)
- [Learning a Probabilistic Latent Space of Object Shapes via 3D Generative-Adversarial Modeling](https://mlsanity.com/paper/1610.07584/) (2016)
- [LION: Latent Point Diffusion Models for 3D Shape Generation](https://mlsanity.com/paper/2210.06978/) (2022)
- [Tackling the Generative Learning Trilemma with Denoising Diffusion GANs](https://mlsanity.com/paper/2112.07804/) (2021)
- [PointFlow: 3D Point Cloud Generation with Continuous Normalizing Flows](https://mlsanity.com/paper/1906.12320/) (2019)
- [PolyGen: An Autoregressive Generative Model of 3D Meshes](https://mlsanity.com/paper/2002.10880/) (2020)
- [GANs Trained by a Two Time-Scale Update Rule Converge to a Local Nash Equilibrium](https://mlsanity.com/paper/1706.08500/) (2017)
- [AutoSDF: Shape Priors for 3D Completion, Reconstruction and Generation](https://mlsanity.com/paper/2203.09516/) (2022)
- [Shape As Points: A Differentiable Poisson Solver](https://mlsanity.com/paper/2106.03452/) (2021)
- [Neural Wavelet-domain Diffusion for 3D Shape Generation](https://mlsanity.com/paper/2209.08725/) (2022)
- [SDM-NET: Deep Generative Network for Structured Deformable Mesh](https://mlsanity.com/paper/1908.04520/) (2019)
- [Neural Cages for Detail-Preserving 3D Deformations](https://mlsanity.com/paper/1912.06395/) (2019)
- [SDF-StyleGAN: Implicit SDF-Based StyleGAN for 3D Shape Generation](https://mlsanity.com/paper/2206.12055/) (2022)
- [Robust Watertight Manifold Surface Generation Method for ShapeNet Models](https://mlsanity.com/paper/1802.01698/) (2018)
- [ARAPReg: An As-Rigid-As Possible Regularization Loss for Learning Deformable Shape Generators](https://mlsanity.com/paper/2108.09432/) (2021)
- [DeepMetaHandles: Learning Deformation Meta-Handles of 3D Meshes with Biharmonic Coordinates](https://mlsanity.com/paper/2102.09105/) (2021)
- [Neural Template: Topology-aware Reconstruction and Disentangled Generation of 3D Meshes](https://mlsanity.com/paper/2206.04942/) (2022)
- [ShapeFlow: Learnable Deformations Among 3D Shapes](https://mlsanity.com/paper/2006.07982/) (2020)
- [Neural Jacobian Fields: Learning Intrinsic Mappings of Arbitrary Meshes](https://mlsanity.com/paper/2205.02904/) (2022)
- [Morig: Motion-aware rigging of character meshes from point clouds](https://mlsanity.com/paper/2210.09463/) (2022)
- [ShapeAssembly: Learning to Generate Programs for 3D Shape Structure Synthesis](https://mlsanity.com/paper/2009.08026/) (2020)
- [GLASS: Geometric Latent Augmentation for Shape Spaces](https://mlsanity.com/paper/2108.03225/) (2021)

## Built on by (most cited first, 6 of 6)

- [Garment3DGen: 3D Garment Stylization and Texture Generation](https://mlsanity.com/paper/2403.18816/) (2024)
- [MeshUp: Multi-Target Mesh Deformation via Blended Score Distillation](https://mlsanity.com/paper/2408.14899/) (2024)
- [Geometry in Style: 3D Stylization via Surface Normal Deformation](https://mlsanity.com/paper/2503.23241/) (2025)
- [NeuROK: Generative 4D Neural Object Kinematics](https://mlsanity.com/paper/2605.30347/) (2026)
- [Mat'ern Noise for Triangulation-Agnostic Flow Matching on Meshes](https://mlsanity.com/paper/2605.19305/) (2026)
- [ARAPDiffusion: ARAP Regularization for Diffusion-Based Deformable Shape Space Learning](https://mlsanity.com/paper/2606.06887/) (2026)

## Abstract (arXiv)

Exploring variations of 3D shapes is a time-consuming process in traditional 3D modeling tools. Deep generative models of 3D shapes often feature continuous latent spaces that can, in principle, be used to explore potential variations starting from a set of input shapes. In practice, doing so can be problematic: latent spaces are high dimensional and hard to visualize, contain shapes that are not relevant to the input shapes, and linear paths through them often lead to sub-optimal shape transitions. Furthermore, one would ideally be able to explore variations in the original high-quality meshes used to train the generative model, not its lower-quality output geometry. In this paper, we present a method to explore variations among a given set of landmark shapes by constructing a mapping from an easily-navigable 2D exploration space to a subspace of a pre-trained generative model. We first describe how to find a mapping that spans the set of input landmark shapes and exhibits smooth variations between them. We then show how to turn the variations in this subspace into deformation fields, to transfer those variations to high-quality meshes for the landmark shapes. Our results show that our method can produce visually-pleasing and easily-navigable 2D exploration spaces for several different shape categories, especially as compared to prior work on learning deformation spaces for 3D shapes.