# Deep Manifold Prior

arXiv: https://arxiv.org/abs/2004.04242 · HTML: https://mlsanity.com/paper/2004.04242/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Apr 2020.

## Built on by (most cited first, 9 of 9)

- [Neural Kernel Surface Reconstruction](https://mlsanity.com/paper/2305.19590/) (2023)
- [Neural Fields as Learnable Kernels for 3D Reconstruction](https://mlsanity.com/paper/2111.13674/) (2021)
- [Surface Reconstruction from Point Clouds by Learning Predictive Context Priors](https://mlsanity.com/paper/2204.11015/) (2022)
- [Surface Reconstruction from Point Clouds: A Survey and a Benchmark](https://mlsanity.com/paper/2205.02413/) (2022)
- [Garment Recovery with Shape and Deformation Priors](https://mlsanity.com/paper/2311.10356/) (2023)
- [SCoDA: Domain Adaptive Shape Completion for Real Scans](https://mlsanity.com/paper/2304.10179/) (2023)
- [Registered and Segmented Deformable Object Reconstruction from a Single View Point Cloud](https://mlsanity.com/paper/2311.07357/) (2023)
- [NSANet: Noise Seeking Attention Network](https://mlsanity.com/paper/2302.13392/) (2023)
- [Spatio-Temporal Garment Reconstruction Using Diffusion Mapping via Pattern Coordinates](https://mlsanity.com/paper/2602.24043/) (2026)

## Abstract (arXiv)

We present a prior for manifold structured data, such as surfaces of 3D shapes, where deep neural networks are adopted to reconstruct a target shape using gradient descent starting from a random initialization. We show that surfaces generated this way are smooth, with limiting behavior characterized by Gaussian processes, and we mathematically derive such properties for fully-connected as well as convolutional networks. We demonstrate our method in a variety of manifold reconstruction applications, such as point cloud denoising and interpolation, achieving considerably better results against competitive baselines while requiring no training data. We also show that when training data is available, our method allows developing alternate parametrizations of surfaces under the framework of AtlasNet, leading to a compact network architecture and better reconstruction results on standard image to shape reconstruction benchmarks.