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 does not always generalize and may lead to
poor-quality renderings. In addition, for real-world scenes, they rely on a
good initial point cloud to perform well. In this work, we rethink 3D Gaussians
as random samples 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 are
strikingly similar to a Stochastic Langevin Gradient Descent (SGLD) update. As
with MCMC, samples are nothing but past visit locations, adding new Gaussians
under our framework can simply be realized without heuristics as placing
Gaussians at existing Gaussian locations. To encourage using fewer Gaussians
for efficiency, we introduce an L1-regularizer on the 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.

3D 高斯喷洒作为神经渲染的一种方法，当前的方法依赖于精心设计的克隆和分裂策略来放置高斯函数，这些方法往往无法泛化并且可能导致质量较低的渲染。本研究提出将 3D 高斯函数视为从描述场景物理表示的基础概率分布中随机采样得到的蒙特卡洛采样，通过这种方法，我们展示了 3D 高斯函数的更新与随机 Langevin 梯度下降更新的惊人相似性。我们的方法在提高渲染质量、轻松控制高斯函数数量和抵抗初始化方面取得了良好效果。