# Curvature-Regularized Variational Autoencoder for 3D Scene Reconstruction from Sparse Depth

arXiv: https://arxiv.org/abs/2512.05783 · HTML: https://mlsanity.com/paper/2512.05783/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 46 references that are in the map.
- First posted on arXiv 5 Dec 2025.

## Builds on (most cited first, 29 of 29)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [pixelNeRF: Neural Radiance Fields from One or Few Images](https://mlsanity.com/paper/2012.02190/) (2020)
- [Magic3D: High-Resolution Text-to-3D Content Creation](https://mlsanity.com/paper/2211.10440/) (2022)
- [Mixed Precision Training](https://mlsanity.com/paper/1710.03740/) (2017)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Volume Rendering of Neural Implicit Surfaces](https://mlsanity.com/paper/2106.12052/) (2021)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [IBRNet: Learning Multi-View Image-Based Rendering](https://mlsanity.com/paper/2102.13090/) (2021)
- [Zip-NeRF: Anti-Aliased Grid-Based Neural Radiance Fields](https://mlsanity.com/paper/2304.06706/) (2023)
- [NVAE: A Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2007.03898/) (2020)
- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)
- [Generating Sentences from a Continuous Space](https://mlsanity.com/paper/1511.06349/) (2015)
- [Learning a Probabilistic Latent Space of Object Shapes via 3D Generative-Adversarial Modeling](https://mlsanity.com/paper/1610.07584/) (2016)
- [Predicting Depth, Surface Normals and Semantic Labels with a Common Multi-Scale Convolutional Architecture](https://mlsanity.com/paper/1411.4734/) (2014)
- [Semantic Scene Completion from a Single Depth Image](https://mlsanity.com/paper/1611.08974/) (2016)
- [GET3D: A Generative Model of High Quality 3D Textured Shapes Learned from Images](https://mlsanity.com/paper/2209.11163/) (2022)
- [MonoScene: Monocular 3D Semantic Scene Completion](https://mlsanity.com/paper/2112.00726/) (2021)
- [Implicit Functions in Feature Space for 3D Shape Reconstruction and Completion](https://mlsanity.com/paper/2003.01456/) (2020)
- [PENet: Towards Precise and Efficient Image Guided Depth Completion](https://mlsanity.com/paper/2103.00783/) (2021)
- [CompletionFormer: Depth Completion with Convolutions and Vision Transformers](https://mlsanity.com/paper/2304.13030/) (2023)
- [Preventing Posterior Collapse with delta-VAEs](https://mlsanity.com/paper/1901.03416/) (2019)
- [OccDepth: A Depth-Aware Method for 3D Semantic Scene Completion](https://mlsanity.com/paper/2302.13540/) (2023)
- [Uncertainty-Aware CNNs for Depth Completion: Uncertainty from Beginning to End](https://mlsanity.com/paper/2006.03349/) (2020)
- [VConv-DAE: Deep Volumetric Shape Learning Without Object Labels](https://mlsanity.com/paper/1604.03755/) (2016)

## Abstract (arXiv)

When depth sensors provide only 5% of needed measurements, reconstructing complete 3D scenes becomes difficult. Autonomous vehicles and robots cannot tolerate the geometric errors that sparse reconstruction introduces. We propose curvature regularization through a discrete Laplacian operator, achieving 18.1% better reconstruction accuracy than standard variational autoencoders. Our contribution challenges an implicit assumption in geometric deep learning: that combining multiple geometric constraints improves performance. A single well-designed regularization term not only matches but exceeds the effectiveness of complex multi-term formulations. The discrete Laplacian offers stable gradients and noise suppression with just 15% training overhead and zero inference cost. Code and models are available at https://github.com/Maryousefi/GeoVAE-3D.