# TutteNet: Injective 3D Deformations by Composition of 2D Mesh Deformations

arXiv: https://arxiv.org/abs/2406.12121 · HTML: https://mlsanity.com/paper/2406.12121/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 62 of its 95 references that are in the map.
- First posted on arXiv 17 Jun 2024.

## Builds on (most cited first, 30 of 62)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [AMASS: Archive of Motion Capture as Surface Shapes](https://mlsanity.com/paper/1904.03278/) (2019)
- [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020)
- [4D Gaussian Splatting for Real-Time Dynamic Scene Rendering](https://mlsanity.com/paper/2310.08528/) (2023)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [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)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [Neural Body: Implicit Neural Representations with Structured Latent Codes for Novel View Synthesis of Dynamic Humans](https://mlsanity.com/paper/2012.15838/) (2020)
- [Nerfstudio: A Modular Framework for Neural Radiance Field Development](https://mlsanity.com/paper/2302.04264/) (2023)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [PointFlow: 3D Point Cloud Generation with Continuous Normalizing Flows](https://mlsanity.com/paper/1906.12320/) (2019)
- [HumanNeRF: Free-viewpoint Rendering of Moving People from Monocular Video](https://mlsanity.com/paper/2201.04127/) (2022)
- [Non-Rigid Neural Radiance Fields: Reconstruction and Novel View Synthesis of a Dynamic Scene From Monocular Video](https://mlsanity.com/paper/2012.12247/) (2020)
- [Dynamic View Synthesis from Dynamic Monocular Video](https://mlsanity.com/paper/2105.06468/) (2021)
- [Invertible Residual Networks](https://mlsanity.com/paper/1811.00995/) (2018)
- [Learning Category-Specific Mesh Reconstruction from Image Collections](https://mlsanity.com/paper/1803.07549/) (2018)
- [MADE: Masked Autoencoder for Distribution Estimation](https://mlsanity.com/paper/1502.03509/) (2015)
- [NeuMan: Neural Human Radiance Field from a Single Video](https://mlsanity.com/paper/2203.12575/) (2022)
- [Learned Initializations for Optimizing Coordinate-Based Neural Representations](https://mlsanity.com/paper/2012.02189/) (2020)
- [A-NeRF: Articulated Neural Radiance Fields for Learning Human Shape, Appearance, and Pose](https://mlsanity.com/paper/2102.06199/) (2021)
- [Editing Conditional Radiance Fields](https://mlsanity.com/paper/2105.06466/) (2021)

## Built on by (most cited first, 3 of 3)

- [PoissonNet: A Local-Global Approach for Learning on Surfaces](https://mlsanity.com/paper/2510.14146/) (2025)
- [Handle-based Mesh Deformation Guided By Vision Language Model](https://mlsanity.com/paper/2506.04562/) (2025)
- [GenSP: Consistent Spherical Parameterization via Learning Shape Generative Models](https://mlsanity.com/paper/2607.00492/) (2026)

## Abstract (arXiv)

This work proposes a novel representation of injective deformations of 3D space, which overcomes existing limitations of injective methods: inaccuracy, lack of robustness, and incompatibility with general learning and optimization frameworks. The core idea is to reduce the problem to a deep composition of multiple 2D mesh-based piecewise-linear maps. Namely, we build differentiable layers that produce mesh deformations through Tutte's embedding (guaranteed to be injective in 2D), and compose these layers over different planes to create complex 3D injective deformations of the 3D volume. We show our method provides the ability to efficiently and accurately optimize and learn complex deformations, outperforming other injective approaches. As a main application, we produce complex and artifact-free NeRF and SDF deformations.