# Conditional-Flow NeRF: Accurate 3D Modelling with Reliable Uncertainty Quantification

arXiv: https://arxiv.org/abs/2203.10192 · HTML: https://mlsanity.com/paper/2203.10192/

## Key facts

- Cited by 73 papers in the map (data through 14 Oct 2026).
- Builds on 56 of its 71 references that are in the map.
- First posted on arXiv 18 Mar 2022.

## Builds on (most cited first, 30 of 56)

- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [pixelNeRF: Neural Radiance Fields from One or Few Images](https://mlsanity.com/paper/2012.02190/) (2020)
- [D-NeRF: Neural Radiance Fields for Dynamic Scenes](https://mlsanity.com/paper/2011.13961/) (2020)
- [Depth Map Prediction from a Single Image using a Multi-Scale Deep Network](https://mlsanity.com/paper/1406.2283/) (2014)
- [NeRF in the Wild: Neural Radiance Fields for Unconstrained Photo Collections](https://mlsanity.com/paper/2008.02268/) (2020)
- [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020)
- [Neural Sparse Voxel Fields](https://mlsanity.com/paper/2007.11571/) (2020)
- [Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations](https://mlsanity.com/paper/1906.01618/) (2019)
- [NeRF++: Analyzing and Improving Neural Radiance Fields](https://mlsanity.com/paper/2010.07492/) (2020)
- [Neural Scene Flow Fields for Space-Time View Synthesis of Dynamic Scenes](https://mlsanity.com/paper/2011.13084/) (2020)
- [Depth-supervised NeRF: Fewer Views and Faster Training for Free](https://mlsanity.com/paper/2107.02791/) (2021)
- [GRAF: Generative Radiance Fields for 3D-Aware Image Synthesis](https://mlsanity.com/paper/2007.02442/) (2020)
- [RegNeRF: Regularizing Neural Radiance Fields for View Synthesis from Sparse Inputs](https://mlsanity.com/paper/2112.00724/) (2021)
- [Predictive Uncertainty Estimation via Prior Networks](https://mlsanity.com/paper/1802.10501/) (2018)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [Using Self-Supervised Learning Can Improve Model Robustness and Uncertainty](https://mlsanity.com/paper/1906.12340/) (2019)
- [PointFlow: 3D Point Cloud Generation with Continuous Normalizing Flows](https://mlsanity.com/paper/1906.12320/) (2019)
- [Dynamic Neural Radiance Fields for Monocular 4D Facial Avatar Reconstruction](https://mlsanity.com/paper/2012.03065/) (2020)
- [INeRF: Inverting Neural Radiance Fields for Pose Estimation](https://mlsanity.com/paper/2012.05877/) (2020)
- [Learned Initializations for Optimizing Coordinate-Based Neural Representations](https://mlsanity.com/paper/2012.02189/) (2020)
- [A-NeRF: Articulated Neural Radiance Fields for Learning Human Shape, Appearance, and Pose](https://mlsanity.com/paper/2102.06199/) (2021)
- [DONeRF: Towards Real-Time Rendering of Compact Neural Radiance Fields using Depth Oracle Networks](https://mlsanity.com/paper/2103.03231/) (2021)

## Built on by (most cited first, 30 of 73)

- [PUP 3D-GS: Principled Uncertainty Pruning for 3D Gaussian Splatting](https://mlsanity.com/paper/2406.10219/) (2024)
- [Bayes' Rays: Uncertainty Quantification for Neural Radiance Fields](https://mlsanity.com/paper/2309.03185/) (2023)
- [FisherRF: Active View Selection and Uncertainty Quantification for Radiance Fields using Fisher Information](https://mlsanity.com/paper/2311.17874/) (2023)
- [Density-aware NeRF Ensembles: Quantifying Predictive Uncertainty in Neural Radiance Fields](https://mlsanity.com/paper/2209.08718/) (2022)
- [PhyRecon: Physically Plausible Neural Scene Reconstruction](https://mlsanity.com/paper/2404.16666/) (2024)
- [Deceptive-NeRF/3DGS: Diffusion-Generated Pseudo-Observations for High-Quality Sparse-View Reconstruction](https://mlsanity.com/paper/2305.15171/) (2023)
- [Fast Learning Radiance Fields by Shooting Much Fewer Rays](https://mlsanity.com/paper/2208.06821/) (2022)
- [Active Neural Mapping](https://mlsanity.com/paper/2308.16246/) (2023)
- [FlipNeRF: Flipped Reflection Rays for Few-shot Novel View Synthesis](https://mlsanity.com/paper/2306.17723/) (2023)
- [Drone-assisted Road Gaussian Splatting with Cross-view Uncertainty](https://mlsanity.com/paper/2408.15242/) (2024)
- [Modeling uncertainty for Gaussian Splatting](https://mlsanity.com/paper/2403.18476/) (2024)
- [DebSDF: Delving into the Details and Bias of Neural Indoor Scene Reconstruction](https://mlsanity.com/paper/2308.15536/) (2023)
- [Skyfall-GS: Synthesizing Immersive 3D Urban Scenes from Satellite Imagery](https://mlsanity.com/paper/2510.15869/) (2025)
- [Estimating 3D Uncertainty Field: Quantifying Uncertainty for Neural Radiance Fields](https://mlsanity.com/paper/2311.01815/) (2023)
- [ProbNeRF: Uncertainty-Aware Inference of 3D Shapes from 2D Images](https://mlsanity.com/paper/2210.17415/) (2022)
- [Leveraging Neural Radiance Fields for Uncertainty-Aware Visual Localization](https://mlsanity.com/paper/2310.06984/) (2023)
- [UP-NeRF: Unconstrained Pose-Prior-Free Neural Radiance Fields](https://mlsanity.com/paper/2311.03784/) (2023)
- [Neural Radiance Field-based Visual Rendering: A Comprehensive Review](https://mlsanity.com/paper/2404.00714/) (2024)
- [Manifold Sampling for Differentiable Uncertainty in Radiance Fields](https://mlsanity.com/paper/2409.12661/) (2024)
- [Neural Radiance Fields for the Real World: A Survey](https://mlsanity.com/paper/2501.13104/) (2025)
- [Sources of Uncertainty in 3D Scene Reconstruction](https://mlsanity.com/paper/2409.06407/) (2024)
- [Multi-view 3D Object Reconstruction and Uncertainty Modelling with Neural Shape Prior](https://mlsanity.com/paper/2306.11739/) (2023)
- [Bayesian NeRF: Quantifying Uncertainty with Volume Density for Neural Implicit Fields](https://mlsanity.com/paper/2404.06727/) (2024)
- [Multimodal LLM Guided Exploration and Active Mapping using Fisher Information](https://mlsanity.com/paper/2410.17422/) (2024)
- [UC-NeRF: Uncertainty-aware Conditional Neural Radiance Fields from Endoscopic Sparse Views](https://mlsanity.com/paper/2409.02917/) (2024)
- [Learning with Unreliability: Fast Few-shot Voxel Radiance Fields with Relative Geometric Consistency](https://mlsanity.com/paper/2403.17638/) (2024)
- [Regularized Multi-Decoder Ensemble for an Error-Aware Scene Representation Network](https://mlsanity.com/paper/2407.19082/) (2024)
- [Few-shot NeRF by Adaptive Rendering Loss Regularization](https://mlsanity.com/paper/2410.17839/) (2024)
- [These Magic Moments: Differentiable Uncertainty Quantification of Radiance Field Models](https://mlsanity.com/paper/2503.14665/) (2025)
- [PRIMU: Uncertainty Estimation for Novel Views in Gaussian Splatting from Primitive-Based Representations of Error and Coverage](https://mlsanity.com/paper/2508.02443/) (2025)

## Abstract (arXiv)

A critical limitation of current methods based on Neural Radiance Fields (NeRF) is that they are unable to quantify the uncertainty associated with the learned appearance and geometry of the scene. This information is paramount in real applications such as medical diagnosis or autonomous driving where, to reduce potentially catastrophic failures, the confidence on the model outputs must be included into the decision-making process. In this context, we introduce Conditional-Flow NeRF (CF-NeRF), a novel probabilistic framework to incorporate uncertainty quantification into NeRF-based approaches. For this purpose, our method learns a distribution over all possible radiance fields modelling which is used to quantify the uncertainty associated with the modelled scene. In contrast to previous approaches enforcing strong constraints over the radiance field distribution, CF-NeRF learns it in a flexible and fully data-driven manner by coupling Latent Variable Modelling and Conditional Normalizing Flows. This strategy allows to obtain reliable uncertainty estimation while preserving model expressivity. Compared to previous state-of-the-art methods proposed for uncertainty quantification in NeRF, our experiments show that the proposed method achieves significantly lower prediction errors and more reliable uncertainty values for synthetic novel view and depth-map estimation.