Neural Product Importance Sampling via Warp Composition

TL;DR

This paper introduces a learning-based importance sampling method using normalizing flows to efficiently approximate complex illumination integrals in photorealistic rendering, reducing variance and improving sampling accuracy.

Contribution

It proposes a novel warp composition approach combining neural spline flows and environment map discretization for better importance sampling of illumination products.

Findings

Significant variance reduction demonstrated on complex scenes.

Efficient sampling of environment and material terms with normalizing flows.

Improved rendering quality and reduced noise in photorealistic images.

Abstract

Achieving high efficiency in modern photorealistic rendering hinges on using Monte Carlo sampling distributions that closely approximate the illumination integral estimated for every pixel. Samples are typically generated from a set of simple distributions, each targeting a different factor in the integrand, which are combined via multiple importance sampling. The resulting mixture distribution can be far from the actual product of all factors, leading to sub-optimal variance even for direct-illumination estimation. We present a learning-based method that uses normalizing flows to efficiently importance sample illumination product integrals, e.g., the product of environment lighting and material terms. Our sampler composes a flow head warp with an emitter tail warp. The small conditional head warp is represented by a neural spline flow, while the large unconditional tail is discretized per environment map and its evaluation is instant. If the conditioning is low-dimensional, the head warp can be also discretized to achieve even better performance. We demonstrate variance reduction over prior methods on a range of applications comprising complex geometry, materials and illumination.