Ray-tracing-based 3D Gaussian splatting (3DGS) enjoys the generality of supporting non-pinhole camera models and relightable formulations. However, they are usually lacking in performance, partially due to the need for depth-based sorting of all intersecting Gaussians along the traced rays.

In this paper, we introduce a sorting-free differentiable stochastic formulation for ray-traced 3DGS, enabling efficient reconstruction and rendering of both standard and relightable 3DGS scenes. For standard 3DGS, our method offers performance comparable to rasterization-based 3DGS and outperforms sorting-based ray tracing. For relightable 3DGS, our technique provides higher-quality reconstructions and renderings thanks to the accurate shadow and shading computation provided by per-Gaussian shading via fully ray-traced shadow rays.