Horseshoe Splatting: Handling Structural Sparsity for Uncertainty-Aware Gaussian-Splatting Radiance Field Rendering

This repository contains the official open-source implementation of the paper "Horseshoe Splatting: Handling Structural Sparsity for Uncertainty-Aware Gaussian-Splatting Radiance Field Rendering", accepted to ICLR 2026.

Horseshoe Splatting is a Bayesian extension of 3D Gaussian Splatting (3DGS) that addresses structured sparsity in per-splat covariances (e.g., axis-wise variances and pairwise correlations) while providing calibrated uncertainty for novel-view rendering. A global-local Horseshoe prior adaptively shrinks noise-dominated covariance components and preserves salient structures. With a factorized variational inference scheme, the method enables efficient Monte Carlo rendering and pixel-wise posterior uncertainty estimation with minimal overhead, while maintaining strong rendering quality and runtime.

Paper link: OpenReview (ICLR 2026)

Framework

Requirements

Hardware Requirements

CUDA-ready GPU with Compute Capability 7.0+

Software Requirements

Conda (recommended for easy setup)

C++ Compiler for PyTorch extensions

CUDA SDK 11 for PyTorch extensions

C++ Compiler and CUDA SDK must be compatible

Usage

Cloning the Repository

Please clone with submodules (The repository will be public after the paper is accepted)

# SSH
git clone git@github.com:HKU-MedAI/Horseshe-Splatting.git --recursive

or

# HTTPS
git clone https://github.com/HKU-MedAI/Horseshe-Splatting.git --recursive

Setup

We provide conda environment file to creat experiment environment:

conda env create --file environment.yml
conda activate hs_splatting

We test our code on ubuntu system, please refer to original 3DGS repo about the potential error building the environment or running on windows.

Preparing Dataset

The LF dataset and LLFF dataset files are provided here: LF dataset, LLFF dataset.

Please unzip and put them under the a dataset folder:

├──dataset
│   │  
│   ├──── LF
│   └──── nerf_llff_data

Running

To train and evaluate the image quality and the image/depth uncertainty on LF dataset:

sh scripts/train_render_lf.sh

To train and evaluate the image quality and image uncertainty quality on LLFF dataset:

sh scripts/train_render_llff.sh

To perform the active training on LLFF dataset:

sh scripts/active_llff.sh

Citation

If you find this work useful, please cite:

@inproceedings{wuhorseshoe,
  title={Horseshoe Splatting: Handling Structural Sparsity for Uncertainty-Aware Gaussian-Splatting Radiance Field Rendering},
  author={Wu, Feng and Chan, Tsai Hor and Chen, Yihang and Zhu, Lingting and Yin, Guosheng and Yu, Lequan},
  booktitle={The Fourteenth International Conference on Learning Representations}
}