# Enhanced Importance Sampling through Latent Space Exploration in Normalizing Flows

arXiv: https://arxiv.org/abs/2501.03394 · HTML: https://mlsanity.com/paper/2501.03394/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 32 references that are in the map.
- First posted on arXiv 6 Jan 2025.

## Builds on (most cited first, 17 of 17)

- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Reliable Fidelity and Diversity Metrics for Generative Models](https://mlsanity.com/paper/2002.09797/) (2020)
- [Learning Likelihoods with Conditional Normalizing Flows](https://mlsanity.com/paper/1912.00042/) (2019)
- [Neural Importance Sampling](https://mlsanity.com/paper/1808.03856/) (2018)
- [Information Theoretic Model Predictive Control: Theory and Applications to Autonomous Driving](https://mlsanity.com/paper/1707.02342/) (2017)
- [NeuTra-lizing Bad Geometry in Hamiltonian Monte Carlo Using Neural Transport](https://mlsanity.com/paper/1903.03704/) (2019)
- [A Survey of Algorithms for Black-Box Safety Validation of Cyber-Physical Systems](https://mlsanity.com/paper/2005.02979/) (2020)
- [Composing Normalizing Flows for Inverse Problems](https://mlsanity.com/paper/2002.11743/) (2020)
- [Neural Bridge Sampling for Evaluating Safety-Critical Autonomous Systems](https://mlsanity.com/paper/2008.10581/) (2020)
- [Featurized Density Ratio Estimation](https://mlsanity.com/paper/2107.02212/) (2021)
- [A RAD approach to deep mixture models](https://mlsanity.com/paper/1903.07714/) (2019)
- [Normalizing flow sampling with Langevin dynamics in the latent space](https://mlsanity.com/paper/2305.12149/) (2023)

## Built on by (most cited first, 1 of 1)

- [Quantifying Behavioral Tails in Black-Box Language Models](https://mlsanity.com/paper/2609.33638/) (2026)

## Abstract (arXiv)

Importance sampling is a rare event simulation technique used in Monte Carlo simulations to bias the sampling distribution towards the rare event of interest. By assigning appropriate weights to sampled points, importance sampling allows for more efficient estimation of rare events or tails of distributions. However, importance sampling can fail when the proposal distribution does not effectively cover the target distribution. In this work, we propose a method for more efficient sampling by updating the proposal distribution in the latent space of a normalizing flow. Normalizing flows learn an invertible mapping from a target distribution to a simpler latent distribution. The latent space can be more easily explored during the search for a proposal distribution, and samples from the proposal distribution are recovered in the space of the target distribution via the invertible mapping. We empirically validate our methodology on simulated robotics applications such as autonomous racing and aircraft ground collision avoidance.