# Sampling for Model Predictive Trajectory Planning in Autonomous Driving using Normalizing Flows

arXiv: https://arxiv.org/abs/2404.09657 · HTML: https://mlsanity.com/paper/2404.09657/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Imitation-learning end-to-end planners, one of 9 directions in End-to-end autonomous driving.
- Builds on 11 of its 21 references that are in the map.
- First posted on arXiv 15 Apr 2024.

## Placed in

- End-to-end autonomous driving / [Imitation-learning end-to-end planners](https://mlsanity.com/driving/imitation-learning-end-to-end-planners/)

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

- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Large Scale Interactive Motion Forecasting for Autonomous Driving : The Waymo Open Motion Dataset](https://mlsanity.com/paper/2104.10133/) (2021)
- [Residual Flows for Invertible Generative Modeling](https://mlsanity.com/paper/1906.02735/) (2019)
- [A Survey of Motion Planning and Control Techniques for Self-driving Urban Vehicles](https://mlsanity.com/paper/1604.07446/) (2016)
- [Information Theoretic Model Predictive Control: Theory and Applications to Autonomous Driving](https://mlsanity.com/paper/1707.02342/) (2017)
- [Autonomous Vehicles on the Edge: A Survey on Autonomous Vehicle Racing](https://mlsanity.com/paper/2202.07008/) (2022)
- [normflows: A PyTorch Package for Normalizing Flows](https://mlsanity.com/paper/2302.12014/) (2023)
- [Variational Inference MPC using Normalizing Flows and Out-of-Distribution Projection](https://mlsanity.com/paper/2205.04667/) (2022)
- [Smooth Model Predictive Path Integral Control without Smoothing](https://mlsanity.com/paper/2112.09988/) (2021)
- [Learning Sampling Distributions for Model Predictive Control](https://mlsanity.com/paper/2212.02587/) (2022)
- [Imitative Planning using Conditional Normalizing Flow](https://mlsanity.com/paper/2007.16162/) (2020)

## Built on by (most cited first, 2 of 2)

- [Generative AI for Autonomous Driving: A Review](https://mlsanity.com/paper/2505.15863/) (2025)
- [Generative Model Predictive Control in Manufacturing Processes: A Review](https://mlsanity.com/paper/2511.17865/) (2025)

## Abstract (arXiv)

Alongside optimization-based planners, sampling-based approaches are often used in trajectory planning for autonomous driving due to their simplicity. Model predictive path integral control is a framework that builds upon optimization principles while incorporating stochastic sampling of input trajectories. This paper investigates several sampling approaches for trajectory generation. In this context, normalizing flows originating from the field of variational inference are considered for the generation of sampling distributions, as they model transformations of simple to more complex distributions. Accordingly, learning-based normalizing flow models are trained for a more efficient exploration of the input domain for the task at hand. The developed algorithm and the proposed sampling distributions are evaluated in two simulation scenarios.