# Modeling uncertainty for Gaussian Splatting

arXiv: https://arxiv.org/abs/2403.18476 · HTML: https://mlsanity.com/paper/2403.18476/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 27 references that are in the map.
- First posted on arXiv 27 Mar 2024.

## Builds on (most cited first, 16 of 16)

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [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)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [NeRF in the Wild: Neural Radiance Fields for Unconstrained Photo Collections](https://mlsanity.com/paper/2008.02268/) (2020)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [PointFlow: 3D Point Cloud Generation with Continuous Normalizing Flows](https://mlsanity.com/paper/1906.12320/) (2019)
- [Hands-on Bayesian Neural Networks -- a Tutorial for Deep Learning Users](https://mlsanity.com/paper/2007.06823/) (2020)
- [Evaluating Scalable Bayesian Deep Learning Methods for Robust Computer Vision](https://mlsanity.com/paper/1906.01620/) (2019)
- [Geometry Uncertainty Projection Network for Monocular 3D Object Detection](https://mlsanity.com/paper/2107.13774/) (2021)
- [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)
- [Conditional-Flow NeRF: Accurate 3D Modelling with Reliable Uncertainty Quantification](https://mlsanity.com/paper/2203.10192/) (2022)
- [Density-aware NeRF Ensembles: Quantifying Predictive Uncertainty in Neural Radiance Fields](https://mlsanity.com/paper/2209.08718/) (2022)
- [Estimating 3D Uncertainty Field: Quantifying Uncertainty for Neural Radiance Fields](https://mlsanity.com/paper/2311.01815/) (2023)
- [FG-NeRF: Flow-GAN based Probabilistic Neural Radiance Field for Independence-Assumption-Free Uncertainty Estimation](https://mlsanity.com/paper/2309.16364/) (2023)

## Built on by (most cited first, 19 of 19)

- [4D Gaussian Splatting in the Wild with Uncertainty-Aware Regularization](https://mlsanity.com/paper/2411.08879/) (2024)
- [Drone-assisted Road Gaussian Splatting with Cross-view Uncertainty](https://mlsanity.com/paper/2408.15242/) (2024)
- [Modeling Uncertainty in 3D Gaussian Splatting through Continuous Semantic Splatting](https://mlsanity.com/paper/2411.02547/) (2024)
- [PhysGS: Bayesian-Inferred Gaussian Splatting for Physical Property Estimation](https://mlsanity.com/paper/2511.18570/) (2025)
- [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)
- [Predictive Photometric Uncertainty in Gaussian Splatting for Novel View Synthesis](https://mlsanity.com/paper/2603.22786/) (2026)
- [Auto3R: Automated 3D Reconstruction and Scanning via Data-driven Uncertainty Quantification](https://mlsanity.com/paper/2512.04528/) (2025)
- [Uncertainty-Aware Diffusion Guided Refinement of 3D Scenes](https://mlsanity.com/paper/2503.15742/) (2025)
- [VarSplat: Uncertainty-aware 3D Gaussian Splatting for Robust RGB-D SLAM](https://mlsanity.com/paper/2603.09673/) (2026)
- [GP-4DGS: Probabilistic 4D Gaussian Splatting from Monocular Video via Variational Gaussian Processes](https://mlsanity.com/paper/2604.02915/) (2026)
- [Do Flat Minima Improve Sparse Novel View Synthesis?](https://mlsanity.com/paper/2511.17918/) (2025)
- [FaithFusion: Harmonizing Reconstruction and Generation via Pixel-wise Information Gain](https://mlsanity.com/paper/2511.21113/) (2025)
- [ConfCtrl: Enabling Precise Camera Control in Video Diffusion via Confidence-Aware Interpolation](https://mlsanity.com/paper/2603.09819/) (2026)
- [RIGI: Rectifying Image-to-3D Generation Inconsistency via Uncertainty-aware Learning](https://mlsanity.com/paper/2411.18866/) (2024)
- [Camera Splatting for Continuous View Optimization](https://mlsanity.com/paper/2509.15677/) (2025)
- [λ-VAE: Variance Equalization for Posterior Collapse](https://mlsanity.com/paper/2607.05531/) (2026)
- [VCURF: Virtual Camera-based Uncertainty of Radiance Fields](https://mlsanity.com/paper/2610.04076/) (2026)
- [SteadySplats: Resampling of Low-Variance Gaussians for High-Fidelity Stochastic Rendering](https://mlsanity.com/paper/2610.05576/) (2026)

## Abstract (arXiv)

We present Stochastic Gaussian Splatting (SGS): the first framework for uncertainty estimation using Gaussian Splatting (GS). GS recently advanced the novel-view synthesis field by achieving impressive reconstruction quality at a fraction of the computational cost of Neural Radiance Fields (NeRF). However, contrary to the latter, it still lacks the ability to provide information about the confidence associated with their outputs. To address this limitation, in this paper, we introduce a Variational Inference-based approach that seamlessly integrates uncertainty prediction into the common rendering pipeline of GS. Additionally, we introduce the Area Under Sparsification Error (AUSE) as a new term in the loss function, enabling optimization of uncertainty estimation alongside image reconstruction. Experimental results on the LLFF dataset demonstrate that our method outperforms existing approaches in terms of both image rendering quality and uncertainty estimation accuracy. Overall, our framework equips practitioners with valuable insights into the reliability of synthesized views, facilitating safer decision-making in real-world applications.