Neural Importance Sampling

Thomas Müller, Brian McWilliams, Fabrice Rousselle, Markus Gross, Jan Novák

Transaction on Graphics (presented at SIGGRAPH 2019), vol. 38, no. 145

Our 32-bin piecewise-linear (4-th column) and 32-bin piecewise-quadratic (5-th column) coupling layers achieve superior performance compared to affine (multiply-add) coupling layers [Dinh et al. 2016] on low-dimensional density-estimation problems. The false-colored distributions were obtained by optimizing KL divergence with uniformly drawn samples (weighted by the reference value) over the 2D image domain.

abstract

We propose to use deep neural networks for generating samples in Monte Carlo integration. Our work is based on non-linear independent component analysis, 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 stochastic estimates of the target distribution. Our approach enables fast and accurate inference and efficient sample generation independent of the dimensionality of the integration domain. We demonstrate the benefits of our approach for generating natural images and in two applications to light-transport simulation. First, we show how to learn joint path-sampling densities in primary sample space and how to importance sample multi-dimensional path prefixes thereof. Second, we use our technique to extract conditional directional densities driven by the triple product of the rendering equation, and leverage them for path guiding. In all applications, our approach yields on-par or higher performance at equal sample count than competing techniques.

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bibtex

@article{mueller2019neural,
	author = {Thomas M\"{u}ller and Brian McWilliams and Fabrice Rousselle and Markus Gross and Jan Nov\'{a}k},
	title = {Neural Importance Sampling},
	journal = {ACM Trans. Graph.},
	issue_date = {October 2019},
	volume = {38},
	number = {5},
	month = oct,
	year = {2019},
	issn = {0730-0301},
	pages = {145:1--145:19},
	articleno = {145},
	numpages = {19},
	url = {http://doi.acm.org/10.1145/3341156},
	doi = {10.1145/3341156},
	acmid = {3341156},
	publisher = {ACM},
	address = {New York, NY, USA},
	keywords = {Monte Carlo, deep learning, importance sampling, normalizing flows, path guiding, rendering},
}