# Depth-guided NeRF Training via Earth Mover's Distance

arXiv: https://arxiv.org/abs/2403.13206 · HTML: https://mlsanity.com/paper/2403.13206/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 35 references that are in the map.
- First posted on arXiv 19 Mar 2024.

## Builds on (most cited first, 28 of 28)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [ScanNet: Richly-annotated 3D Reconstructions of Indoor Scenes](https://mlsanity.com/paper/1702.04405/) (2017)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Vision Transformers for Dense Prediction](https://mlsanity.com/paper/2103.13413/) (2021)
- [pixelNeRF: Neural Radiance Fields from One or Few Images](https://mlsanity.com/paper/2012.02190/) (2020)
- [Towards Robust Monocular Depth Estimation: Mixing Datasets for Zero-shot Cross-dataset Transfer](https://mlsanity.com/paper/1907.01341/) (2019)
- [Depth Anything: Unleashing the Power of Large-Scale Unlabeled Data](https://mlsanity.com/paper/2401.10891/) (2024)
- [Depth-supervised NeRF: Fewer Views and Faster Training for Free](https://mlsanity.com/paper/2107.02791/) (2021)
- [ZoeDepth: Zero-shot Transfer by Combining Relative and Metric Depth](https://mlsanity.com/paper/2302.12288/) (2023)
- [RegNeRF: Regularizing Neural Radiance Fields for View Synthesis from Sparse Inputs](https://mlsanity.com/paper/2112.00724/) (2021)
- [NICE-SLAM: Neural Implicit Scalable Encoding for SLAM](https://mlsanity.com/paper/2112.12130/) (2021)
- [Putting NeRF on a Diet: Semantically Consistent Few-Shot View Synthesis](https://mlsanity.com/paper/2104.00677/) (2021)
- [Metric3D: Towards Zero-shot Metric 3D Prediction from A Single Image](https://mlsanity.com/paper/2307.10984/) (2023)
- [Dense Depth Priors for Neural Radiance Fields from Sparse Input Views](https://mlsanity.com/paper/2112.03288/) (2021)
- [SparseNeRF: Distilling Depth Ranking for Few-shot Novel View Synthesis](https://mlsanity.com/paper/2303.16196/) (2023)
- [Learning to Recover 3D Scene Shape from a Single Image](https://mlsanity.com/paper/2012.09365/) (2020)
- [Vision-Only Robot Navigation in a Neural Radiance World](https://mlsanity.com/paper/2110.00168/) (2021)
- [NeW CRFs: Neural Window Fully-connected CRFs for Monocular Depth Estimation](https://mlsanity.com/paper/2203.01502/) (2022)
- [Neural Rendering for Stereo 3D Reconstruction of Deformable Tissues in Robotic Surgery](https://mlsanity.com/paper/2206.15255/) (2022)
- [DepthFormer: Exploiting Long-Range Correlation and Local Information for Accurate Monocular Depth Estimation](https://mlsanity.com/paper/2203.14211/) (2022)
- [Revealing the Dark Secrets of Masked Image Modeling](https://mlsanity.com/paper/2205.13543/) (2022)
- [Indoor Semantic Segmentation using depth information](https://mlsanity.com/paper/1301.3572/) (2013)
- [SCADE: NeRFs from Space Carving with Ambiguity-Aware Depth Estimates](https://mlsanity.com/paper/2303.13582/) (2023)
- [DaRF: Boosting Radiance Fields from Sparse Inputs with Monocular Depth Adaptation](https://mlsanity.com/paper/2305.19201/) (2023)
- [DINER: Depth-aware Image-based NEural Radiance fields](https://mlsanity.com/paper/2211.16630/) (2022)
- [One-Shot Neural Fields for 3D Object Understanding](https://mlsanity.com/paper/2210.12126/) (2022)

## Built on by (most cited first, 2 of 2)

- [Uncertainty-guided Optimal Transport in Depth Supervised Sparse-View 3D Gaussian](https://mlsanity.com/paper/2405.19657/) (2024)
- [NeVStereo: A NeRF-Driven NVS-Stereo Architecture for High-Fidelity 3D Tasks](https://mlsanity.com/paper/2602.05423/) (2026)

## Abstract (arXiv)

Neural Radiance Fields (NeRFs) are trained to minimize the rendering loss of predicted viewpoints. However, the photometric loss often does not provide enough information to disambiguate between different possible geometries yielding the same image. Previous work has thus incorporated depth supervision during NeRF training, leveraging dense predictions from pre-trained depth networks as pseudo-ground truth. While these depth priors are assumed to be perfect once filtered for noise, in practice, their accuracy is more challenging to capture. This work proposes a novel approach to uncertainty in depth priors for NeRF supervision. Instead of using custom-trained depth or uncertainty priors, we use off-the-shelf pretrained diffusion models to predict depth and capture uncertainty during the denoising process. Because we know that depth priors are prone to errors, we propose to supervise the ray termination distance distribution with Earth Mover's Distance instead of enforcing the rendered depth to replicate the depth prior exactly through L2-loss. Our depth-guided NeRF outperforms all baselines on standard depth metrics by a large margin while maintaining performance on photometric measures.