  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.
