# Bayesian NeRF: Quantifying Uncertainty with Volume Density for Neural Implicit Fields

arXiv: https://arxiv.org/abs/2404.06727 · HTML: https://mlsanity.com/paper/2404.06727/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 51 references that are in the map.
- First posted on arXiv 10 Apr 2024.

## Builds on (most cited first, 30 of 37)

- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [pixelNeRF: Neural Radiance Fields from One or Few Images](https://mlsanity.com/paper/2012.02190/) (2020)
- [Zero-1-to-3: Zero-shot One Image to 3D Object](https://mlsanity.com/paper/2303.11328/) (2023)
- [NeRF in the Wild: Neural Radiance Fields for Unconstrained Photo Collections](https://mlsanity.com/paper/2008.02268/) (2020)
- [The Replica Dataset: A Digital Replica of Indoor Spaces](https://mlsanity.com/paper/1906.05797/) (2019)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [Block-NeRF: Scalable Large Scene Neural View Synthesis](https://mlsanity.com/paper/2202.05263/) (2022)
- [Zip-NeRF: Anti-Aliased Grid-Based Neural Radiance Fields](https://mlsanity.com/paper/2304.06706/) (2023)
- [NICE-SLAM: Neural Implicit Scalable Encoding for SLAM](https://mlsanity.com/paper/2112.12130/) (2021)
- [iMAP: Implicit Mapping and Positioning in Real-Time](https://mlsanity.com/paper/2103.12352/) (2021)
- [Mega-NeRF: Scalable Construction of Large-Scale NeRFs for Virtual Fly-Throughs](https://mlsanity.com/paper/2112.10703/) (2021)
- [CLIP-NeRF: Text-and-Image Driven Manipulation of Neural Radiance Fields](https://mlsanity.com/paper/2112.05139/) (2021)
- [FreeNeRF: Improving Few-shot Neural Rendering with Free Frequency Regularization](https://mlsanity.com/paper/2303.07418/) (2023)
- [NeRF-Editing: Geometry Editing of Neural Radiance Fields](https://mlsanity.com/paper/2205.04978/) (2022)
- [NeRF-SLAM: Real-Time Dense Monocular SLAM with Neural Radiance Fields](https://mlsanity.com/paper/2210.13641/) (2022)
- [Co-SLAM: Joint Coordinate and Sparse Parametric Encodings for Neural Real-Time SLAM](https://mlsanity.com/paper/2304.14377/) (2023)
- [MARS: An Instance-aware, Modular and Realistic Simulator for Autonomous Driving](https://mlsanity.com/paper/2307.15058/) (2023)
- [Vox-Fusion: Dense Tracking and Mapping with Voxel-based Neural Implicit Representation](https://mlsanity.com/paper/2210.15858/) (2022)
- [Tri-MipRF: Tri-Mip Representation for Efficient Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2307.11335/) (2023)
- [ActiveNeRF: Learning where to See with Uncertainty Estimation](https://mlsanity.com/paper/2209.08546/) (2022)
- [Bayes' Rays: Uncertainty Quantification for Neural Radiance Fields](https://mlsanity.com/paper/2309.03185/) (2023)
- [Stochastic Neural Radiance Fields: Quantifying Uncertainty in Implicit 3D Representations](https://mlsanity.com/paper/2109.02123/) (2021)
- [FoV-NeRF: Foveated Neural Radiance Fields for Virtual Reality](https://mlsanity.com/paper/2103.16365/) (2021)
- [Conditional-Flow NeRF: Accurate 3D Modelling with Reliable Uncertainty Quantification](https://mlsanity.com/paper/2203.10192/) (2022)
- [vMAP: Vectorised Object Mapping for Neural Field SLAM](https://mlsanity.com/paper/2302.01838/) (2023)
- [Neural LiDAR Fields for Novel View Synthesis](https://mlsanity.com/paper/2305.01643/) (2023)
- [Density-aware NeRF Ensembles: Quantifying Predictive Uncertainty in Neural Radiance Fields](https://mlsanity.com/paper/2209.08718/) (2022)

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

- [PhysGS: Bayesian-Inferred Gaussian Splatting for Physical Property Estimation](https://mlsanity.com/paper/2511.18570/) (2025)
- [Uncertainty-driven 3D Gaussian Splatting Active Mapping via Anisotropic Visibility Field](https://mlsanity.com/paper/2605.30342/) (2026)
- [VarSplat: Uncertainty-aware 3D Gaussian Splatting for Robust RGB-D SLAM](https://mlsanity.com/paper/2603.09673/) (2026)
- [SA-ResGS: Self-Augmented Residual 3D Gaussian Splatting for Next Best View Selection](https://mlsanity.com/paper/2601.03024/) (2026)
- [ObjSplat: Geometry-Aware Gaussian Surfels for Active Object Reconstruction](https://mlsanity.com/paper/2601.06997/) (2026)
- [BayesSDF: Surface-Based Laplacian Uncertainty Estimation for 3D Geometry with Neural Signed Distance Fields](https://mlsanity.com/paper/2507.06269/) (2025)
- [Do Flat Minima Improve Sparse Novel View Synthesis?](https://mlsanity.com/paper/2511.17918/) (2025)
- [PCM-NeRF: Probabilistic Camera Modeling for Neural Radiance Fields under Pose Uncertainty](https://mlsanity.com/paper/2604.17831/) (2026)
- [NeuDonatello: Uncertainty-Aware Framework for Accurate Neural SDF Learning](https://mlsanity.com/paper/2608.26504/) (2026)

## Abstract (arXiv)

We present a Bayesian Neural Radiance Field (NeRF), which explicitly quantifies uncertainty in the volume density by modeling uncertainty in the occupancy, without the need for additional networks, making it particularly suited for challenging observations and uncontrolled image environments. NeRF diverges from traditional geometric methods by providing an enriched scene representation, rendering color and density in 3D space from various viewpoints. However, NeRF encounters limitations in addressing uncertainties solely through geometric structure information, leading to inaccuracies when interpreting scenes with insufficient real-world observations. While previous efforts have relied on auxiliary networks, we propose a series of formulation extensions to NeRF that manage uncertainties in density, both color and density, and occupancy, all without the need for additional networks. In experiments, we show that our method significantly enhances performance on RGB and depth images in the comprehensive dataset. Given that uncertainty modeling aligns well with the inherently uncertain environments of Simultaneous Localization and Mapping (SLAM), we applied our approach to SLAM systems and observed notable improvements in mapping and tracking performance. These results confirm the effectiveness of our Bayesian NeRF approach in quantifying uncertainty based on geometric structure, making it a robust solution for challenging real-world scenarios.