# Plug-and-Play PDE Optimization for 3D Gaussian Splatting: Toward High-Quality Rendering and Reconstruction

arXiv: https://arxiv.org/abs/2509.13938 · HTML: https://mlsanity.com/paper/2509.13938/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Sep 2025.

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

- [VeloGauss: Learning Physically Consistent Gaussian Velocity Fields from Videos](https://mlsanity.com/paper/2605.10567/) (2026)
- [StreamSplat: Streaming Feed-Forward 3D Gaussian Splatting](https://mlsanity.com/paper/2608.01659/) (2026)

## Abstract (arXiv)

3D Gaussian Splatting (3DGS) has revolutionized radiance field reconstruction by achieving high-quality novel view synthesis with fast rendering speed, introducing 3D Gaussian primitives to represent the scene. However, 3DGS encounters blurring and floaters when applied to complex scenes, caused by the reconstruction of redundant and ambiguous geometric structures. We attribute this issue to the unstable optimization of the Gaussians. To address this limitation, we present a plug-and-play PDE-based optimization method that overcomes the optimization constraints of 3DGS-based approaches in various tasks, such as novel view synthesis and surface reconstruction. Firstly, we theoretically derive that the 3DGS optimization procedure can be modeled as a PDE, and introduce a viscous term to ensure stable optimization. Secondly, we use the Material Point Method (MPM) to obtain a stable numerical solution of the PDE, which enhances both global and local constraints. Additionally, an effective Gaussian densification strategy and particle constraints are introduced to ensure fine-grained details. Extensive qualitative and quantitative experiments confirm that our method achieves state-of-the-art rendering and reconstruction quality.