StochasticSplats: Stochastic Rasterization for Sorting-Free 3D Gaussian Splatting

TL;DR

This work addresses the bottleneck and artifacts of depth-sorted 3D Gaussian splatting by introducing stochastic transparency, an unbiased Monte Carlo estimator of the volume rendering equation, which enables sorting-free, end-to-end differentiable rendering. The authors derive forward and backward passes for stochastic rendering, provide a practical three-pass gradient scheme, and propose strategies to remove popping artifacts, including a simplified per-fragment depth approach and full volumetric intermixing via free-flight distance sampling. They implement the method in OpenGL (with CUDA benchmarks for comparison) and demonstrate substantial speedups (up to 2–4x faster) with competitive visual fidelity, while enabling dynamic quality-cost trade-offs through sampling. The approach offers portability, compatibility with standard graphics pipelines, and applicability to open-vocabulary localization tasks, making stochastic splats suitable for latency-critical applications and differentiable optimization in 3D radiance fields.

Abstract

3D Gaussian splatting (3DGS) is a popular radiance field method, with many application-specific extensions. Most variants rely on the same core algorithm: depth-sorting of Gaussian splats then rasterizing in primitive order. This ensures correct alpha compositing, but can cause rendering artifacts due to built-in approximations. Moreover, for a fixed representation, sorted rendering offers little control over render cost and visual fidelity. For example, and counter-intuitively, rendering a lower-resolution image is not necessarily faster. In this work, we address the above limitations by combining 3D Gaussian splatting with stochastic rasterization. Concretely, we leverage an unbiased Monte Carlo estimator of the volume rendering equation. This removes the need for sorting, and allows for accurate 3D blending of overlapping Gaussians. The number of Monte Carlo samples further imbues 3DGS with a way to trade off computation time and quality. We implement our method using OpenGL shaders, enabling efficient rendering on modern GPU hardware. At a reasonable visual quality, our method renders more than four times faster than sorted rasterization.

Figures (10)

• Figure 1: Teaser -- We render a 3DGS radiance field using an unbiased Monte Carlo estimator of the volume rendering equation. Unlike prior radiance field approaches, our method does not require sorted back-to-front rendering. This results in fast, portable, and pop-free rendering that is easy to implement. The number of Monte Carlo samples per pixel allows a trade-off between interactivity and visual quality, similar to physically-based rendering. From left to right, we increase the number of samples per pixel, which increases visual fidelity at a predictable increase in rendering cost. We report the mean square error (MSE) and render time on an NVIDIA RTX 4090.
• Figure 2: Blending vs. stochastic -- We visualize a 1D and 3D example of the different ways to compute transparency. Two foreground Gaussians are composited on a white background.
• Figure 3: Gradient validation -- We compare alpha blending gradients to our stochastic estimator with 128 and 512 SPP. Red and blue colors encode positive and negative values, respectively. Our estimator accurately approximates the alpha blending gradients.
• Figure 4: Popping in 3DGS -- (left) As sorting in 3DGS is done with respect to the $z$ distance of the Gaussian mean from the camera, a small camera rotation can cause visible "popping" artifacts (i.e., sudden pixel color changes). (right) StopThePop stopthepop corrects for this behavior by associating a surface with each Gaussian, and determining the depth $z$ per-fragment (dashed line), rather than per-Gaussian. Our solution leads to visually comparable results, but approximates this surface linearly (solid line), so that per-fragment depth $z$ can be computed efficiently in hardware.
• Figure 5: Fully volumetric intermixing -- While alpha blending (left) suffers from popping and "pop-free" variants (middle) show discontinuities, our full volumetric intermixing (right) accurately composes overlapping Gaussians.