# Neural Importance Sampling Source: [Neural Importance Sampling]() Collection index: [llms.txt]() Data updated: 2025-10-25T21:45:30.461Z Authors: Thomas M\\"uller, Brian McWilliams, Fabrice Rousselle, Markus Gross, Jan Nov\\'ak Published: 2018-08-11T20:12:49.000Z ## 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. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Counterfactual Sampling on SIMPSON-NLIN Markovian diffeomorphic (test)](): Counterfactual Sampling; SIMPSON-NLIN Markovian diffeomorphic (test); ESP: 0. - [Counterfactual Sampling on NAPKIN Semi-Markovian continuous (test)](): Counterfactual Sampling; NAPKIN Semi-Markovian continuous (test); ESP: 0. - [Counterfactual Sampling on FAIRNESS-XW Regional canonical (test)](): Counterfactual Sampling; FAIRNESS-XW Regional canonical (test); ESP: 9.4. ## Original sources and implementation [Original paper]() [PDF]()