# Gaussians on their Way: Wasserstein-Constrained 4D Gaussian Splatting with State-Space Modeling

arXiv: https://arxiv.org/abs/2412.00333 · HTML: https://mlsanity.com/paper/2412.00333/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 46 of its 73 references that are in the map.
- First posted on arXiv 30 Nov 2024.

## Builds on (most cited first, 30 of 46)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [D-NeRF: Neural Radiance Fields for Dynamic Scenes](https://mlsanity.com/paper/2011.13961/) (2020)
- [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020)
- [4D Gaussian Splatting for Real-Time Dynamic Scene Rendering](https://mlsanity.com/paper/2310.08528/) (2023)
- [Simple Online and Realtime Tracking](https://mlsanity.com/paper/1602.00763/) (2016)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Deformable 3D Gaussians for High-Fidelity Monocular Dynamic Scene Reconstruction](https://mlsanity.com/paper/2309.13101/) (2023)
- [Neural Scene Flow Fields for Space-Time View Synthesis of Dynamic Scenes](https://mlsanity.com/paper/2011.13084/) (2020)
- [K-Planes: Explicit Radiance Fields in Space, Time, and Appearance](https://mlsanity.com/paper/2301.10241/) (2023)
- [Dynamic 3D Gaussians: Tracking by Persistent Dynamic View Synthesis](https://mlsanity.com/paper/2308.09713/) (2023)
- [Local Light Field Fusion: Practical View Synthesis with Prescriptive Sampling Guidelines](https://mlsanity.com/paper/1905.00889/) (2019)
- [HexPlane: A Fast Representation for Dynamic Scenes](https://mlsanity.com/paper/2301.09632/) (2023)
- [HumanNeRF: Free-viewpoint Rendering of Moving People from Monocular Video](https://mlsanity.com/paper/2201.04127/) (2022)
- [Real-time Photorealistic Dynamic Scene Representation and Rendering with 4D Gaussian Splatting](https://mlsanity.com/paper/2310.10642/) (2023)
- [Dynamic View Synthesis from Dynamic Monocular Video](https://mlsanity.com/paper/2105.06468/) (2021)
- [Animatable Neural Radiance Fields for Modeling Dynamic Human Bodies](https://mlsanity.com/paper/2105.02872/) (2021)
- [SC-GS: Sparse-Controlled Gaussian Splatting for Editable Dynamic Scenes](https://mlsanity.com/paper/2312.14937/) (2023)
- [Spacetime Gaussian Feature Splatting for Real-Time Dynamic View Synthesis](https://mlsanity.com/paper/2312.16812/) (2023)
- [Shape of Motion: 4D Reconstruction from a Single Video](https://mlsanity.com/paper/2407.13764/) (2024)
- [Free View Synthesis](https://mlsanity.com/paper/2008.05511/) (2020)
- [Tensor4D : Efficient Neural 4D Decomposition for High-fidelity Dynamic Reconstruction and Rendering](https://mlsanity.com/paper/2211.11610/) (2022)
- [HyperNeRF: A Higher-Dimensional Representation for Topologically Varying Neural Radiance Fields](https://mlsanity.com/paper/2106.13228/) (2021)
- [Statistical Aspects of Wasserstein Distances](https://mlsanity.com/paper/1806.05500/) (2018)
- [3DGS-Avatar: Animatable Avatars via Deformable 3D Gaussian Splatting](https://mlsanity.com/paper/2312.09228/) (2023)
- [4D-Rotor Gaussian Splatting: Towards Efficient Novel View Synthesis for Dynamic Scenes](https://mlsanity.com/paper/2402.03307/) (2024)
- [HyperReel: High-Fidelity 6-DoF Video with Ray-Conditioned Sampling](https://mlsanity.com/paper/2301.02238/) (2023)
- [GauHuman: Articulated Gaussian Splatting from Monocular Human Videos](https://mlsanity.com/paper/2312.02973/) (2023)
- [Stable View Synthesis](https://mlsanity.com/paper/2011.07233/) (2020)

## Built on by (most cited first, 1 of 1)

- [Bringing a Personal Point of View: Evaluating Dynamic 3D Gaussian Splatting for Egocentric Scene Reconstruction](https://mlsanity.com/paper/2604.23803/) (2026)

## Abstract (arXiv)

Dynamic scene rendering has taken a leap forward with the rise of 4D Gaussian Splatting, but there's still one elusive challenge: how to make 3D Gaussians move through time as naturally as they would in the real world, all while keeping the motion smooth and consistent. In this paper, we unveil a fresh approach that blends state-space modeling with Wasserstein geometry, paving the way for a more fluid and coherent representation of dynamic scenes. We introduce a State Consistency Filter that merges prior predictions with the current observations, enabling Gaussians to stay true to their way over time. We also employ Wasserstein distance regularization to ensure smooth, consistent updates of Gaussian parameters, reducing motion artifacts. Lastly, we leverage Wasserstein geometry to capture both translational motion and shape deformations, creating a more physically plausible model for dynamic scenes. Our approach guides Gaussians along their natural way in the Wasserstein space, achieving smoother, more realistic motion and stronger temporal coherence. Experimental results show significant improvements in rendering quality and efficiency, outperforming current state-of-the-art techniques.