# Neural Wavelet-domain Diffusion for 3D Shape Generation, Inversion, and Manipulation

arXiv: https://arxiv.org/abs/2302.00190 · HTML: https://mlsanity.com/paper/2302.00190/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- Builds on 67 of its 90 references that are in the map.
- First posted on arXiv 1 Feb 2023.

## Builds on (most cited first, 30 of 67)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [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)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [RePaint: Inpainting using Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.09865/) (2022)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [Neural Sparse Voxel Fields](https://mlsanity.com/paper/2007.11571/) (2020)
- [Diffusion Probabilistic Models for 3D Point Cloud Generation](https://mlsanity.com/paper/2103.01458/) (2021)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [Differentiable Volumetric Rendering: Learning Implicit 3D Representations without 3D Supervision](https://mlsanity.com/paper/1912.07372/) (2019)
- [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)
- [Designing an Encoder for StyleGAN Image Manipulation](https://mlsanity.com/paper/2102.02766/) (2021)
- [AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generation](https://mlsanity.com/paper/1802.05384/) (2018)
- [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)
- [Diffusion Autoencoders: Toward a Meaningful and Decodable Representation](https://mlsanity.com/paper/2111.15640/) (2021)
- [GET3D: A Generative Model of High Quality 3D Textured Shapes Learned from Images](https://mlsanity.com/paper/2209.11163/) (2022)
- [Neural Geometric Level of Detail: Real-time Rendering with Implicit 3D Shapes](https://mlsanity.com/paper/2101.10994/) (2021)
- [SAL: Sign Agnostic Learning of Shapes from Raw Data](https://mlsanity.com/paper/1911.10414/) (2019)
- [GAN Inversion: A Survey](https://mlsanity.com/paper/2101.05278/) (2021)
- [StyleFlow: Attribute-conditioned Exploration of StyleGAN-Generated Images using Conditional Continuous Normalizing Flows](https://mlsanity.com/paper/2008.02401/) (2020)
- [Generative Visual Manipulation on the Natural Image Manifold](https://mlsanity.com/paper/1609.03552/) (2016)
- [Implicit Functions in Feature Space for 3D Shape Reconstruction and Completion](https://mlsanity.com/paper/2003.01456/) (2020)

## Built on by (most cited first, 27 of 27)

- [Towards Realistic Scene Generation with LiDAR Diffusion Models](https://mlsanity.com/paper/2404.00815/) (2024)
- [SALAD: Part-Level Latent Diffusion for 3D Shape Generation and Manipulation](https://mlsanity.com/paper/2303.12236/) (2023)
- [Texture Generation on 3D Meshes with Point-UV Diffusion](https://mlsanity.com/paper/2308.10490/) (2023)
- [InstructP2P: Learning to Edit 3D Point Clouds with Text Instructions](https://mlsanity.com/paper/2306.07154/) (2023)
- [LaS-Comp: Zero-shot 3D Completion with Latent-Spatial Consistency](https://mlsanity.com/paper/2602.18735/) (2026)
- [Advances in 3D Neural Stylization: A Survey](https://mlsanity.com/paper/2311.18328/) (2023)
- [CNS-Edit: 3D Shape Editing via Coupled Neural Shape Optimization](https://mlsanity.com/paper/2402.02313/) (2024)
- [Generating 3D House Wireframes with Semantics](https://mlsanity.com/paper/2407.12267/) (2024)
- [Spatial-Frequency U-Net for Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2307.14648/) (2023)
- [CLR-Wire: Towards Continuous Latent Representations for 3D Curve Wireframe Generation](https://mlsanity.com/paper/2504.19174/) (2025)
- [Part-aware Shape Generation with Latent 3D Diffusion of Neural Voxel Fields](https://mlsanity.com/paper/2405.00998/) (2024)
- [SOPHY: Learning to Generate Simulation-Ready Objects with Physical Materials](https://mlsanity.com/paper/2504.12684/) (2025)
- [PEGAsus: 3D Personalization of Geometry and Appearance](https://mlsanity.com/paper/2602.08198/) (2026)
- [Mix3R: Mixing Feed-forward Reconstruction and Generative 3D Priors for Joint Multi-view Aligned 3D Reconstruction and Pose Estimation](https://mlsanity.com/paper/2605.03359/) (2026)
- [WaveletDiff: Multilevel Wavelet Diffusion For Time Series Generation](https://mlsanity.com/paper/2510.11839/) (2025)
- [Deep Sketch-Based 3D Modeling: A Survey](https://mlsanity.com/paper/2603.03287/) (2026)
- [EPS3D: End-to-End Feed-Forward 3D Panoptic Segmentation](https://mlsanity.com/paper/2606.08980/) (2026)
- [View Transformation Robustness for Multi-View 3D Object Reconstruction with Reconstruction Error-Guided View Selection](https://mlsanity.com/paper/2412.11428/) (2024)
- [B-Rep Distance Functions (BR-DF): How to Represent a B-Rep Model by Volumetric Distance Functions?](https://mlsanity.com/paper/2511.14870/) (2025)
- [Spectral Regularization for Diffusion Models](https://mlsanity.com/paper/2603.02447/) (2026)
- [High-Fidelity Medical Shape Generation via Skeletal Latent Diffusion](https://mlsanity.com/paper/2603.07504/) (2026)
- [WonderVerse: Extendable 3D Scene Generation with Video Generative Models](https://mlsanity.com/paper/2503.09160/) (2025)
- [3D Shape Generation: A Survey](https://mlsanity.com/paper/2506.22678/) (2025)
- [CNS-Edit++: Category-Agnostic 3D Editing with Coupled Neural Shape Representation](https://mlsanity.com/paper/2607.16577/) (2026)
- [Fourier-Latent Diffusion for Constrained Generation of Triply Periodic Minimal Surfaces](https://mlsanity.com/paper/2608.02151/) (2026)
- [BTC3D: Blended Tile Conditioning for Detail-Enhancing Image-to-3D Generation](https://mlsanity.com/paper/2609.39709/) (2026)
- [DiDE:Direct Injection with Color-Texture DEcoupling for 3D Stylization](https://mlsanity.com/paper/2610.02044/) (2026)

## Abstract (arXiv)

This paper presents a new approach for 3D shape generation, inversion, and manipulation, through a direct generative modeling on a continuous implicit representation in wavelet domain. Specifically, we propose a compact wavelet representation with a pair of coarse and detail coefficient volumes to implicitly represent 3D shapes via truncated signed distance functions and multi-scale biorthogonal wavelets. Then, we design a pair of neural networks: a diffusion-based generator to produce diverse shapes in the form of the coarse coefficient volumes and a detail predictor to produce compatible detail coefficient volumes for introducing fine structures and details. Further, we may jointly train an encoder network to learn a latent space for inverting shapes, allowing us to enable a rich variety of whole-shape and region-aware shape manipulations. Both quantitative and qualitative experimental results manifest the compelling shape generation, inversion, and manipulation capabilities of our approach over the state-of-the-art methods.