# Neural Wavelet-domain Diffusion for 3D Shape Generation

arXiv: https://arxiv.org/abs/2209.08725 · HTML: https://mlsanity.com/paper/2209.08725/

## Key facts

- Cited by 132 papers in the map (data through 14 Oct 2026).
- Builds on 47 of its 60 references that are in the map.
- First posted on arXiv 19 Sep 2022.

## Builds on (most cited first, 30 of 47)

- [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)
- [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)
- [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)
- [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)
- [Implicit Functions in Feature Space for 3D Shape Reconstruction and Completion](https://mlsanity.com/paper/2003.01456/) (2020)
- [DISN: Deep Implicit Surface Network for High-quality Single-view 3D Reconstruction](https://mlsanity.com/paper/1905.10711/) (2019)
- [Learning Gradient Fields for Shape Generation](https://mlsanity.com/paper/2008.06520/) (2020)
- [Learning a Predictable and Generative Vector Representation for Objects](https://mlsanity.com/paper/1603.08637/) (2016)
- [ShapeFormer: Transformer-based Shape Completion via Sparse Representation](https://mlsanity.com/paper/2201.10326/) (2022)
- [Learning to Infer Implicit Surfaces without 3D Supervision](https://mlsanity.com/paper/1911.00767/) (2019)
- [SoftFlow: Probabilistic Framework for Normalizing Flow on Manifolds](https://mlsanity.com/paper/2006.04604/) (2020)
- [SDF-StyleGAN: Implicit SDF-Based StyleGAN for 3D Shape Generation](https://mlsanity.com/paper/2206.12055/) (2022)

## Built on by (most cited first, 30 of 132)

- [Structured 3D Latents for Scalable and Versatile 3D Generation](https://mlsanity.com/paper/2412.01506/) (2024)
- [3DShape2VecSet: A 3D Shape Representation for Neural Fields and Generative Diffusion Models](https://mlsanity.com/paper/2301.11445/) (2023)
- [MeshGPT: Generating Triangle Meshes with Decoder-Only Transformers](https://mlsanity.com/paper/2311.15475/) (2023)
- [XCube: Large-Scale 3D Generative Modeling using Sparse Voxel Hierarchies](https://mlsanity.com/paper/2312.03806/) (2023)
- [Native and Compact Structured Latents for 3D Generation](https://mlsanity.com/paper/2512.14692/) (2025)
- [DiffuScene: Denoising Diffusion Models for Generative Indoor Scene Synthesis](https://mlsanity.com/paper/2303.14207/) (2023)
- [RenderDiffusion: Image Diffusion for 3D Reconstruction, Inpainting and Generation](https://mlsanity.com/paper/2211.09869/) (2022)
- [Diffusion-SDF: Conditional Generative Modeling of Signed Distance Functions](https://mlsanity.com/paper/2211.13757/) (2022)
- [Locally Attentional SDF Diffusion for Controllable 3D Shape Generation](https://mlsanity.com/paper/2305.04461/) (2023)
- [State of the Art on Diffusion Models for Visual Computing](https://mlsanity.com/paper/2310.07204/) (2023)
- [CraftsMan3D: High-fidelity Mesh Generation with 3D Native Generation and Interactive Geometry Refiner](https://mlsanity.com/paper/2405.14979/) (2024)
- [HoloDiffusion: Training a 3D Diffusion Model using 2D Images](https://mlsanity.com/paper/2303.16509/) (2023)
- [BrepGen: A B-rep Generative Diffusion Model with Structured Latent Geometry](https://mlsanity.com/paper/2401.15563/) (2024)
- [Score-based Diffusion Models in Function Space](https://mlsanity.com/paper/2302.07400/) (2023)
- [SparseFlex: High-Resolution and Arbitrary-Topology 3D Shape Modeling](https://mlsanity.com/paper/2503.21732/) (2025)
- [LooseControl: Lifting ControlNet for Generalized Depth Conditioning](https://mlsanity.com/paper/2312.03079/) (2023)
- [3D-LDM: Neural Implicit 3D Shape Generation with Latent Diffusion Models](https://mlsanity.com/paper/2212.00842/) (2022)
- [SALAD: Part-Level Latent Diffusion for 3D Shape Generation and Manipulation](https://mlsanity.com/paper/2303.12236/) (2023)
- [InstructEdit: Improving Automatic Masks for Diffusion-based Image Editing With User Instructions](https://mlsanity.com/paper/2305.18047/) (2023)
- [Texture Generation on 3D Meshes with Point-UV Diffusion](https://mlsanity.com/paper/2308.10490/) (2023)
- [Advances in 3D Generation: A Survey](https://mlsanity.com/paper/2401.17807/) (2024)
- [OmniPart: Part-Aware 3D Generation with Semantic Decoupling and Structural Cohesion](https://mlsanity.com/paper/2507.06165/) (2025)
- [HoloPart: Generative 3D Part Amodal Segmentation](https://mlsanity.com/paper/2504.07943/) (2025)
- [SceneGen: Single-Image 3D Scene Generation in One Feedforward Pass](https://mlsanity.com/paper/2508.15769/) (2025)
- [Efficient Diffusion Models for Vision: A Survey](https://mlsanity.com/paper/2210.09292/) (2022)
- [PivotMesh: Generic 3D Mesh Generation via Pivot Vertices Guidance](https://mlsanity.com/paper/2405.16890/) (2024)
- [Mosaic-SDF for 3D Generative Models](https://mlsanity.com/paper/2312.09222/) (2023)
- [WaveDM: Wavelet-Based Diffusion Models for Image Restoration](https://mlsanity.com/paper/2305.13819/) (2023)
- [RenAIssance: A Survey into AI Text-to-Image Generation in the Era of Large Model](https://mlsanity.com/paper/2309.00810/) (2023)
- [UniDream: Unifying Diffusion Priors for Relightable Text-to-3D Generation](https://mlsanity.com/paper/2312.08754/) (2023)

## Abstract (arXiv)

This paper presents a new approach for 3D shape generation, enabling 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, and formulate a pair of neural networks: a generator based on the diffusion model to produce diverse shapes in the form of coarse coefficient volumes; and a detail predictor to further produce compatible detail coefficient volumes for enriching the generated shapes with fine structures and details. Both quantitative and qualitative experimental results manifest the superiority of our approach in generating diverse and high-quality shapes with complex topology and structures, clean surfaces, and fine details, exceeding the 3D generation capabilities of the state-of-the-art models.