Practical Gaussian Process Implicit Surfaces with Sparse Convolutions

A fundamental challenge in rendering has been the dichotomy between surface and volume models. Gaussian Process Implicit Surfaces (GPISes) recently provided a unified approach for surfaces, volumes, and the spectrum in between. However, this representation remains impractical due to its high computational cost and mathematical complexity. We address these limitations by reformulating GPISes as procedural noise, eliminating expensive linear system solves while maintaining control over spatial correlations. Our method enables efficient sampling of stochastic realizations and supports flexible conditioning of values and derivatives through pathwise updates. To further enable practical rendering, we derive analytic distributions for surface normals, allowing for variance-reduced light transport via next-event estimation and multiple importance sampling. Our framework achieves efficient, high-quality rendering of stochastic surfaces and volumes with significantly simplified implementations on both CPU and GPU, while preserving the generality of the original GPIS representation.