# 3D Gaussian Splatting as Markov Chain Monte Carlo

arXiv: https://arxiv.org/abs/2404.09591 · HTML: https://mlsanity.com/paper/2404.09591/

## Key facts

- Cited by 217 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 51 references that are in the map.
- First posted on arXiv 15 Apr 2024.

## Builds on (most cited first, 30 of 33)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Mip-NeRF 360: Unbounded Anti-Aliased Neural Radiance Fields](https://mlsanity.com/paper/2111.12077/) (2021)
- [Mip-NeRF: A Multiscale Representation for Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2103.13415/) (2021)
- [pixelNeRF: Neural Radiance Fields from One or Few Images](https://mlsanity.com/paper/2012.02190/) (2020)
- [DUSt3R: Geometric 3D Vision Made Easy](https://mlsanity.com/paper/2312.14132/) (2023)
- [4D Gaussian Splatting for Real-Time Dynamic Scene Rendering](https://mlsanity.com/paper/2310.08528/) (2023)
- [PlenOctrees for Real-time Rendering of Neural Radiance Fields](https://mlsanity.com/paper/2103.14024/) (2021)
- [DreamGaussian: Generative Gaussian Splatting for Efficient 3D Content Creation](https://mlsanity.com/paper/2309.16653/) (2023)
- [Deformable 3D Gaussians for High-Fidelity Monocular Dynamic Scene Reconstruction](https://mlsanity.com/paper/2309.13101/) (2023)
- [pixelSplat: 3D Gaussian Splats from Image Pairs for Scalable Generalizable 3D Reconstruction](https://mlsanity.com/paper/2312.12337/) (2023)
- [Mip-Splatting: Alias-free 3D Gaussian Splatting](https://mlsanity.com/paper/2311.16493/) (2023)
- [Dynamic Neural Radiance Fields for Monocular 4D Facial Avatar Reconstruction](https://mlsanity.com/paper/2012.03065/) (2020)
- [How to Escape Saddle Points Efficiently](https://mlsanity.com/paper/1703.00887/) (2017)
- [Triplane Meets Gaussian Splatting: Fast and Generalizable Single-View 3D Reconstruction with Transformers](https://mlsanity.com/paper/2312.09147/) (2023)
- [Compressed 3D Gaussian Splatting for Accelerated Novel View Synthesis](https://mlsanity.com/paper/2401.02436/) (2023)
- [A Survey on 3D Gaussian Splatting](https://mlsanity.com/paper/2401.03890/) (2024)
- [Generalized Sliced Wasserstein Distances](https://mlsanity.com/paper/1902.00434/) (2019)
- [NeRF: Neural Radiance Field in 3D Vision: A Comprehensive Review (Updated Post-Gaussian Splatting)](https://mlsanity.com/paper/2210.00379/) (2022)
- [HUGS: Human Gaussian Splats](https://mlsanity.com/paper/2311.17910/) (2023)
- [Adding Gradient Noise Improves Learning for Very Deep Networks](https://mlsanity.com/paper/1511.06807/) (2015)
- [Multi-Scale 3D Gaussian Splatting for Anti-Aliased Rendering](https://mlsanity.com/paper/2311.17089/) (2023)
- [Revising Densification in Gaussian Splatting](https://mlsanity.com/paper/2404.06109/) (2024)
- [ShaRF: Shape-conditioned Radiance Fields from a Single View](https://mlsanity.com/paper/2102.08860/) (2021)
- [Bayes' Rays: Uncertainty Quantification for Neural Radiance Fields](https://mlsanity.com/paper/2309.03185/) (2023)
- [MedNeRF: Medical Neural Radiance Fields for Reconstructing 3D-aware CT-Projections from a Single X-ray](https://mlsanity.com/paper/2202.01020/) (2022)
- [GAvatar: Animatable 3D Gaussian Avatars with Implicit Mesh Learning](https://mlsanity.com/paper/2312.11461/) (2023)

## Built on by (most cited first, 30 of 217)

- [gsplat: An Open-Source Library for Gaussian Splatting](https://mlsanity.com/paper/2409.06765/) (2024)
- [Stable Virtual Camera: Generative View Synthesis with Diffusion Models](https://mlsanity.com/paper/2503.14489/) (2025)
- [3DGUT: Enabling Distorted Cameras and Secondary Rays in Gaussian Splatting](https://mlsanity.com/paper/2412.12507/) (2024)
- [3DGS.zip: A survey on 3D Gaussian Splatting Compression Methods](https://mlsanity.com/paper/2407.09510/) (2024)
- [SplatAD: Real-Time Lidar and Camera Rendering with 3D Gaussian Splatting for Autonomous Driving](https://mlsanity.com/paper/2411.16816/) (2024)
- [Triangle Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2505.19175/) (2025)
- [EVER: Exact Volumetric Ellipsoid Rendering for Real-time View Synthesis](https://mlsanity.com/paper/2410.01804/) (2024)
- [3DGS-LM: Faster Gaussian-Splatting Optimization with Levenberg-Marquardt](https://mlsanity.com/paper/2409.12892/) (2024)
- [3DRealCar: An In-the-wild RGB-D Car Dataset with 360-degree Views](https://mlsanity.com/paper/2406.04875/) (2024)
- [MILo: Mesh-In-the-Loop Gaussian Splatting for Detailed and Efficient Surface Reconstruction](https://mlsanity.com/paper/2506.24096/) (2025)
- [Efficient Perspective-Correct 3D Gaussian Splatting Using Hybrid Transparency](https://mlsanity.com/paper/2410.08129/) (2024)
- [Radiant Foam: Real-Time Differentiable Ray Tracing](https://mlsanity.com/paper/2502.01157/) (2025)
- [VR-Splatting: Foveated Radiance Field Rendering via 3D Gaussian Splatting and Neural Points](https://mlsanity.com/paper/2410.17932/) (2024)
- [Luminance-GS: Adapting 3D Gaussian Splatting to Challenging Lighting Conditions with View-Adaptive Curve Adjustment](https://mlsanity.com/paper/2504.01503/) (2025)
- [NerfBaselines: Consistent and Reproducible Evaluation of Novel View Synthesis Methods](https://mlsanity.com/paper/2406.17345/) (2024)
- [BillBoard Splatting (BBSplat): Learnable Textured Primitives for Novel View Synthesis](https://mlsanity.com/paper/2411.08508/) (2024)
- [HiMoR: Monocular Deformable Gaussian Reconstruction with Hierarchical Motion Representation](https://mlsanity.com/paper/2504.06210/) (2025)
- [LinPrim: Linear Primitives for Differentiable Volumetric Rendering](https://mlsanity.com/paper/2501.16312/) (2025)
- [MVGS: Multi-view Regulated Gaussian Splatting for Novel View Synthesis](https://mlsanity.com/paper/2410.02103/) (2024)
- [Optimized Minimal 3D Gaussian Splatting](https://mlsanity.com/paper/2503.16924/) (2025)
- [LoopSparseGS: Loop Based Sparse-View Friendly Gaussian Splatting](https://mlsanity.com/paper/2408.00254/) (2024)
- [Generative Densification: Learning to Densify Gaussians for High-Fidelity Generalizable 3D Reconstruction](https://mlsanity.com/paper/2412.06234/) (2024)
- [VRSplat: Fast and Robust Gaussian Splatting for Virtual Reality](https://mlsanity.com/paper/2505.10144/) (2025)
- [Faster-GS: Analyzing and Improving Gaussian Splatting Optimization](https://mlsanity.com/paper/2602.09999/) (2026)
- [6DGS: Enhanced Direction-Aware Gaussian Splatting for Volumetric Rendering](https://mlsanity.com/paper/2410.04974/) (2024)
- [Efficient Scene Modeling via Structure-Aware and Region-Prioritized 3D Gaussians](https://mlsanity.com/paper/2411.12788/) (2024)
- [DROID-Splat: Combining end-to-end SLAM with 3D Gaussian Splatting](https://mlsanity.com/paper/2411.17660/) (2024)
- [DeSplat: Decomposed Gaussian Splatting for Distractor-Free Rendering](https://mlsanity.com/paper/2411.19756/) (2024)
- [Gaussian Splatting for Efficient Satellite Image Photogrammetry](https://mlsanity.com/paper/2412.13047/) (2024)
- [SceneSplat++: A Large Dataset and Comprehensive Benchmark for Language Gaussian Splatting](https://mlsanity.com/paper/2506.08710/) (2025)

## Abstract (arXiv)

While 3D Gaussian Splatting has recently become popular for neural rendering, current methods rely on carefully engineered cloning and splitting strategies for placing Gaussians, which can lead to poor-quality renderings, and reliance on a good initialization. In this work, we rethink the set of 3D Gaussians as a random sample drawn from an underlying probability distribution describing the physical representation of the scene-in other words, Markov Chain Monte Carlo (MCMC) samples. Under this view, we show that the 3D Gaussian updates can be converted as Stochastic Gradient Langevin Dynamics (SGLD) updates by simply introducing noise. We then rewrite the densification and pruning strategies in 3D Gaussian Splatting as simply a deterministic state transition of MCMC samples, removing these heuristics from the framework. To do so, we revise the 'cloning' of Gaussians into a relocalization scheme that approximately preserves sample probability. To encourage efficient use of Gaussians, we introduce a regularizer that promotes the removal of unused Gaussians. On various standard evaluation scenes, we show that our method provides improved rendering quality, easy control over the number of Gaussians, and robustness to initialization.