# A Flow-Based Generative Model for Rare-Event Simulation

arXiv: https://arxiv.org/abs/2305.07863 · HTML: https://mlsanity.com/paper/2305.07863/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 26 references that are in the map.
- First posted on arXiv 13 May 2023.

## Builds on (most cited first, 11 of 11)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Guided Image Generation with Conditional Invertible Neural Networks](https://mlsanity.com/paper/1907.02392/) (2019)
- [Coupling-based Invertible Neural Networks Are Universal Diffeomorphism Approximators](https://mlsanity.com/paper/2006.11469/) (2020)
- [Latent Normalizing Flows for Discrete Sequences](https://mlsanity.com/paper/1901.10548/) (2019)
- [Conditioning Normalizing Flows for Rare Event Sampling](https://mlsanity.com/paper/2207.14530/) (2022)
- [Certifiable Deep Importance Sampling for Rare-Event Simulation of Black-Box Systems](https://mlsanity.com/paper/2111.02204/) (2021)

## Built on by (most cited first, 5 of 5)

- [Diffusion-Based Failure Sampling for Evaluating Safety-Critical Autonomous Systems](https://mlsanity.com/paper/2406.14761/) (2024)
- [Rare Event Probability Learning by Normalizing Flows](https://mlsanity.com/paper/2310.19167/) (2023)
- [Importance Sampling-Guided Meta-Training for Intelligent Agents in Highly Interactive Environments](https://mlsanity.com/paper/2407.15839/) (2024)
- [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)

Solving decision problems in complex, stochastic environments is often achieved by estimating the expected outcome of decisions via Monte Carlo sampling. However, sampling may overlook rare, but important events, which can severely impact the decision making process. We present a method in which a Normalizing Flow generative model is trained to simulate samples directly from a conditional distribution given that a rare event occurs. By utilizing Coupling Flows, our model can, in principle, approximate any sampling distribution arbitrarily well. By combining the approximation method with Importance Sampling, highly accurate estimates of complicated integrals and expectations can be obtained. We include several examples to demonstrate how the method can be used for efficient sampling and estimation, even in high-dimensional and rare-event settings. We illustrate that by simulating directly from a rare-event distribution significant insight can be gained into the way rare events happen.