# FG-NeRF: Flow-GAN based Probabilistic Neural Radiance Field for Independence-Assumption-Free Uncertainty Estimation

arXiv: https://arxiv.org/abs/2309.16364 · HTML: https://mlsanity.com/paper/2309.16364/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 50 of its 55 references that are in the map.
- First posted on arXiv 28 Sep 2023.

## Builds on (most cited first, 30 of 50)

- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [ScanNet: Richly-annotated 3D Reconstructions of Indoor Scenes](https://mlsanity.com/paper/1702.04405/) (2017)
- [Mip-NeRF: A Multiscale Representation for Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2103.13415/) (2021)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [TensoRF: Tensorial Radiance Fields](https://mlsanity.com/paper/2203.09517/) (2022)
- [NeRF in the Wild: Neural Radiance Fields for Unconstrained Photo Collections](https://mlsanity.com/paper/2008.02268/) (2020)
- [Efficient Geometry-aware 3D Generative Adversarial Networks](https://mlsanity.com/paper/2112.07945/) (2021)
- [Instance Normalization: The Missing Ingredient for Fast Stylization](https://mlsanity.com/paper/1607.08022/) (2016)
- [Volume Rendering of Neural Implicit Surfaces](https://mlsanity.com/paper/2106.12052/) (2021)
- [The Replica Dataset: A Digital Replica of Indoor Spaces](https://mlsanity.com/paper/1906.05797/) (2019)
- [NeRF++: Analyzing and Improving Neural Radiance Fields](https://mlsanity.com/paper/2010.07492/) (2020)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [pi-GAN: Periodic Implicit Generative Adversarial Networks for 3D-Aware Image Synthesis](https://mlsanity.com/paper/2012.00926/) (2020)
- [GRAF: Generative Radiance Fields for 3D-Aware Image Synthesis](https://mlsanity.com/paper/2007.02442/) (2020)
- [Generative Adversarial Networks: An Overview](https://mlsanity.com/paper/1710.07035/) (2017)
- [Predictive Uncertainty Estimation via Prior Networks](https://mlsanity.com/paper/1802.10501/) (2018)
- [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)
- [MonoSDF: Exploring Monocular Geometric Cues for Neural Implicit Surface Reconstruction](https://mlsanity.com/paper/2206.00665/) (2022)
- [In-Place Scene Labelling and Understanding with Implicit Scene Representation](https://mlsanity.com/paper/2103.15875/) (2021)
- [MobileNeRF: Exploiting the Polygon Rasterization Pipeline for Efficient Neural Field Rendering on Mobile Architectures](https://mlsanity.com/paper/2208.00277/) (2022)
- [DONeRF: Towards Real-Time Rendering of Compact Neural Radiance Fields using Depth Oracle Networks](https://mlsanity.com/paper/2103.03231/) (2021)
- [GRAM: Generative Radiance Manifolds for 3D-Aware Image Generation](https://mlsanity.com/paper/2112.08867/) (2021)
- [On the uncertainty of self-supervised monocular depth estimation](https://mlsanity.com/paper/2005.06209/) (2020)

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

- [Modeling uncertainty for Gaussian Splatting](https://mlsanity.com/paper/2403.18476/) (2024)
- [Geometric Neural Process Fields](https://mlsanity.com/paper/2502.02338/) (2025)

## Abstract (arXiv)

Neural radiance fields with stochasticity have garnered significant interest by enabling the sampling of plausible radiance fields and quantifying uncertainty for downstream tasks. Existing works rely on the independence assumption of points in the radiance field or the pixels in input views to obtain tractable forms of the probability density function. However, this assumption inadvertently impacts performance when dealing with intricate geometry and texture. In this work, we propose an independence-assumption-free probabilistic neural radiance field based on Flow-GAN. By combining the generative capability of adversarial learning and the powerful expressivity of normalizing flow, our method explicitly models the density-radiance distribution of the whole scene. We represent our probabilistic NeRF as a mean-shifted probabilistic residual neural model. Our model is trained without an explicit likelihood function, thereby avoiding the independence assumption. Specifically, We downsample the training images with different strides and centers to form fixed-size patches which are used to train the generator with patch-based adversarial learning. Through extensive experiments, our method demonstrates state-of-the-art performance by predicting lower rendering errors and more reliable uncertainty on both synthetic and real-world datasets.