Conditional Resampled Importance Sampling and ReSTIR

Abstract

Recent work on generalized resampled importance sampling (GRIS) enables importance-sampled Monte Carlo integration with random variable weights replacing the usual division by probability density. This enables very flexible spatiotemporal sample reuse, even if neighboring samples (e.g., light paths) have intractable probability densities. Unlike typical Monte Carlo integration, which samples according to some PDF, GRIS instead resamples existing samples. But resampling with GRIS assumes samples have tractable marginal contribution weights, which is problematic if reusing, for example, light subpaths from unidirectionally-sampled paths. Reusing such subpaths requires conditioning by (non-reused) segments of the path prefixes. In this paper, we extend GRIS to conditional probability spaces, showing correctness given certain conditional independence between integration variables and their unbiased contribution weights. We show proper conditioning when using GRIS over randomized conditional domains and how to formulate a joint unbiased contribution weight for unbiased integration. To show our theory has practical impact, we prototype a modified ReSTIR PT with a final gather pass. This reuses subpaths, postponing reuse at least one bounce along each light path. As in photon mapping, such a final gather reduces blotchy artifacts from sample correlation and reduced correlation improves the behavior of modern denoisers on ReSTIR PT signals.