# Neural Importance Sampling

arXiv: https://arxiv.org/abs/1808.03856 · HTML: https://mlsanity.com/paper/1808.03856/

## Key facts

- Cited by 155 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Aug 2018.

## Built on by (most cited first, 30 of 155)

- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Models](https://mlsanity.com/paper/2103.04922/) (2021)
- [Continuous diffusion for categorical data](https://mlsanity.com/paper/2211.15089/) (2022)
- [On Embeddings for Numerical Features in Tabular Deep Learning](https://mlsanity.com/paper/2203.05556/) (2022)
- [Co-SLAM: Joint Coordinate and Sparse Parametric Encodings for Neural Real-Time SLAM](https://mlsanity.com/paper/2304.14377/) (2023)
- [Flow Annealed Importance Sampling Bootstrap](https://mlsanity.com/paper/2208.01893/) (2022)
- [Riemannian Diffusion Models](https://mlsanity.com/paper/2208.07949/) (2022)
- [Flow Matching for Scalable Simulation-Based Inference](https://mlsanity.com/paper/2305.17161/) (2023)
- [Real-time Neural Radiance Caching for Path Tracing](https://mlsanity.com/paper/2106.12372/) (2021)
- [How NeRFs and 3D Gaussian Splatting are Reshaping SLAM: a Survey](https://mlsanity.com/paper/2402.13255/) (2024)
- [A Diffusion Model Framework for Unsupervised Neural Combinatorial Optimization](https://mlsanity.com/paper/2406.01661/) (2024)
- [Diffusion Generative Flow Samplers: Improving learning signals through partial trajectory optimization](https://mlsanity.com/paper/2310.02679/) (2023)
- [normflows: A PyTorch Package for Normalizing Flows](https://mlsanity.com/paper/2302.12014/) (2023)
- [Smooth Normalizing Flows](https://mlsanity.com/paper/2110.00351/) (2021)
- [Densely connected normalizing flows](https://mlsanity.com/paper/2106.04627/) (2021)
- [Neural LerPlane Representations for Fast 4D Reconstruction of Deformable Tissues](https://mlsanity.com/paper/2305.19906/) (2023)
- [VolTeMorph: Realtime, Controllable and Generalisable Animation of Volumetric Representations](https://mlsanity.com/paper/2208.00949/) (2022)
- [Copula Flows for Synthetic Data Generation](https://mlsanity.com/paper/2101.00598/) (2021)
- [Neural Radiosity](https://mlsanity.com/paper/2105.12319/) (2021)
- [Stochastic Normalizing Flows for Inverse Problems: a Markov Chains Viewpoint](https://mlsanity.com/paper/2109.11375/) (2021)
- [Scalable Discrete Diffusion Samplers: Combinatorial Optimization and Statistical Physics](https://mlsanity.com/paper/2502.08696/) (2025)
- [Neural BRDF Representation and Importance Sampling](https://mlsanity.com/paper/2102.05963/) (2021)
- [Neural Importance Sampling for Rapid and Reliable Gravitational-Wave Inference](https://mlsanity.com/paper/2210.05686/) (2022)
- [NARUTO: Neural Active Reconstruction from Uncertain Target Observations](https://mlsanity.com/paper/2402.18771/) (2024)
- [Rigid Body Flows for Sampling Molecular Crystal Structures](https://mlsanity.com/paper/2301.11355/) (2023)
- [Maximum Entropy Reinforcement Learning via Energy-Based Normalizing Flow](https://mlsanity.com/paper/2405.13629/) (2024)
- [Generalized Normalizing Flows via Markov Chains](https://mlsanity.com/paper/2111.12506/) (2021)
- [Gradients should stay on Path: Better Estimators of the Reverse- and Forward KL Divergence for Normalizing Flows](https://mlsanity.com/paper/2207.08219/) (2022)
- [Advances in machine-learning-based sampling motivated by lattice quantum chromodynamics](https://mlsanity.com/paper/2309.01156/) (2023)
- [DNS SLAM: Dense Neural Semantic-Informed SLAM](https://mlsanity.com/paper/2312.00204/) (2023)

## Abstract (arXiv)

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 chi2 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.