Learning to Importance Sample in Primary Sample Space

TL;DR

This paper introduces a neural network-based importance sampling method for Monte Carlo rendering that learns to generate samples with desired densities in the primary sample space, leading to variance reduction.

Contribution

It proposes a novel importance sampling technique using Real NVP neural networks to warp primary sample space, agnostic to underlying rendering algorithms.

Findings

Effective variance reduction demonstrated in practical scenarios

Compatible with various existing rendering techniques

Uses Real NVP for efficient density transformation

Abstract

Importance sampling is one of the most widely used variance reduction strategies in Monte Carlo rendering. In this paper, we propose a novel importance sampling technique that uses a neural network to learn how to sample from a desired density represented by a set of samples. Our approach considers an existing Monte Carlo rendering algorithm as a black box. During a scene-dependent training phase, we learn to generate samples with a desired density in the primary sample space of the rendering algorithm using maximum likelihood estimation. We leverage a recent neural network architecture that was designed to represent real-valued non-volume preserving ('Real NVP') transformations in high dimensional spaces. We use Real NVP to non-linearly warp primary sample space and obtain desired densities. In addition, Real NVP efficiently computes the determinant of the Jacobian of the warp, which is required to implement the change of integration variables implied by the warp. A main advantage of our approach is that it is agnostic of underlying light transport effects, and can be combined with many existing rendering techniques by treating them as a black box. We show that our approach leads to effective variance reduction in several practical scenarios.