# Rare Event Probability Learning by Normalizing Flows

arXiv: https://arxiv.org/abs/2310.19167 · HTML: https://mlsanity.com/paper/2310.19167/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 42 references that are in the map.
- First posted on arXiv 29 Oct 2023.

## Builds on (most cited first, 15 of 15)

- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [SRFlow: Learning the Super-Resolution Space with Normalizing Flow](https://mlsanity.com/paper/2006.14200/) (2020)
- [Neural Importance Sampling](https://mlsanity.com/paper/1808.03856/) (2018)
- [Annealed Flow Transport Monte Carlo](https://mlsanity.com/paper/2102.07501/) (2021)
- [Scalable End-to-End Autonomous Vehicle Testing via Rare-event Simulation](https://mlsanity.com/paper/1811.00145/) (2018)
- [Neural Approximate Sufficient Statistics for Implicit Models](https://mlsanity.com/paper/2010.10079/) (2020)
- [Continual Repeated Annealed Flow Transport Monte Carlo](https://mlsanity.com/paper/2201.13117/) (2022)
- [i-flow: High-dimensional Integration and Sampling with Normalizing Flows](https://mlsanity.com/paper/2001.05486/) (2020)
- [A Flow-Based Generative Model for Rare-Event Simulation](https://mlsanity.com/paper/2305.07863/) (2023)

## Built on by (most cited first, 3 of 3)

- [Rare event modeling with self-regularized normalizing flows: what can we learn from a single failure?](https://mlsanity.com/paper/2502.21110/) (2025)
- [Repulsive normalizing flow mixtures for adaptive importance sampling: reliability analysis of complex systems](https://mlsanity.com/paper/2609.21160/) (2026)
- [Robust Importance Sampling for Rare Events via Constrained Gaussian Mixtures](https://mlsanity.com/paper/2610.07485/) (2026)

## Abstract (arXiv)

A rare event is defined by a low probability of occurrence. Accurate estimation of such small probabilities is of utmost importance across diverse domains. Conventional Monte Carlo methods are inefficient, demanding an exorbitant number of samples to achieve reliable estimates. Inspired by the exact sampling capabilities of normalizing flows, we revisit this challenge and propose normalizing flow assisted importance sampling, termed NOFIS. NOFIS first learns a sequence of proposal distributions associated with predefined nested subset events by minimizing KL divergence losses. Next, it estimates the rare event probability by utilizing importance sampling in conjunction with the last proposal. The efficacy of our NOFIS method is substantiated through comprehensive qualitative visualizations, affirming the optimality of the learned proposal distribution, as well as a series of quantitative experiments encompassing 10 distinct test cases, which highlight NOFIS's superiority over baseline approaches.