SIGGRAPH 2026 · Conference Papers

Adaptive Ray Marching for Rendering
Gaussian Process Implicit Surfaces

A 46× reduction in rendering MSE at equal time for Gaussian Process Implicit Surfaces, via online GP sampling and probabilistic adaptive ray marching.

Zhiqian Zhou1, Dario Seyb2, Shuang Zhao3
1University of California, Irvine   2Valve   3University of Illinois Urbana-Champaign
Paper Paper (compressed) Supplemental Code (available soon) BibTeX
Ground truth rendering of a Gaussian-process bunny
Ground Truth
Our method's rendering of the same bunny
Ours · MSE 0.007
Baseline (Seyb et al. 2024) rendering of the same bunny at equal time
Seyb et al. [2024] · MSE 0.321

Figure 1. GPIS is a probabilistic representation of 3D shapes, bridging the gap between microfacets, participating media and measurement uncertainties. Despite its usefulness, it has been historically challenging to render. Our method accelerates computing the ensemble averaged light transport by orders of magnitude compared to Seyb et al. [2024], by adaptively tracing the Gaussian process and drawing values using an online sampler. The figure renders a bunny-shaped Gaussian field with our method and Seyb et al. [2024] at equal time (7.5 minutes).

Abstract

Gaussian Process Implicit Surfaces (GPIS) represent geometry as a distribution over implicit functions. Modeling an object's appearance as the expected rendering of a GPIS yields a unified framework that captures diverse light-transport effects including microfacet-like reflections and volumetric scattering. Despite this generality, computing GPIS-ray intersections requires sampling conditional multivariate Gaussian distributions along each ray and remains prohibitively expensive.

We introduce an online sampling algorithm that draws these distributions incrementally, and an adaptive marching scheme that takes large steps where the surface is provably absent — minimizing the probability of missed intersections. Together, these ideas reduce rendering MSE by up to 46× at equal time compared to existing methods.

Method

We address the bottleneck of GPIS-ray intersection, by marching along the ray with adaptive step sizes, sampling the Gaussian process incrementally until a sign change in $f$ brackets a zero crossing. An online sampler produces each new value $f(t_i)$ on the fly. The step size $t_{i+1} - t_i$ is then determined automatically so that the probability of skipping over a root stays below a small tolerance. At equal or higher accuracy, the marcher uses far fewer GP samples than the baseline, and reduces computation by about a cubic factor.

Baseline — uniform grid

f t 0
Evenly-spaced evaluation points (Seyb et al. 2024). Values of $f$ are drawn at once from a multivariate Gaussian. This has a high computation cost due to the $\mathcal{O}(n^3)$ complexity from sampling.

Ours — adaptive marching

f t 0
Adaptive marching: we take large yet conservative steps along the function, automatically tightening the steps as approaching a potential surface.

BibTeX

@inproceedings{zhou2026adaptive,
  title     = {Adaptive Ray Marching for Rendering Gaussian Process Implicit Surfaces},
  author    = {Zhou, Zhiqian and Seyb, Dario and Zhao, Shuang},
  booktitle = {SIGGRAPH 2026 Conference Papers},
  year      = {2026},
  publisher = {ACM},
  address   = {Los Angeles, CA, USA},
  doi       = {10.1145/3799902.3811101}
}