Neural Importance Sampling

TL;DR

This paper introduces a neural importance sampling method using extended NICE models with novel transformations and encoding techniques, enabling efficient high-dimensional Monte Carlo integration and applications in image generation and light-transport simulation.

Contribution

It extends NICE with piecewise-polynomial transforms and input encoding, and develops gradient-based optimization for divergence measures tailored to Monte Carlo integration.

Findings

Achieves fast, accurate inference regardless of dimensionality.

Outperforms competing techniques in image generation tasks.

Effective in light-transport simulation and path guiding applications.

Abstract

We propose to use deep neural networks for generating samples in Monte Carlo integration. Our work is based on non-linear independent components estimation (NICE), which we extend in numerous ways to improve performance and enable its application to integration problems. First, we introduce piecewise-polynomial coupling transforms that greatly increase the modeling power of individual coupling layers. Second, we propose to preprocess the inputs of neural networks using one-blob encoding, which stimulates localization of computation and improves inference. Third, we derive a gradient-descent-based optimization for the KL and the $\chi^2$ divergence for the specific application of Monte Carlo integration with unnormalized stochastic estimates of the target distribution. Our approach enables fast and accurate inference and efficient sample generation independently of the dimensionality of the integration domain. We show its benefits on generating natural images and in two applications to light-transport simulation: first, we demonstrate learning of joint path-sampling densities in the primary sample space and importance sampling of multi-dimensional path prefixes thereof. Second, we use our technique to extract conditional directional densities driven by the product of incident illumination and the BSDF in the rendering equation, and we leverage the densities for path guiding. In all applications, our approach yields on-par or higher performance than competing techniques at equal sample count.