# TrajFlow: A Generative Framework for Occupancy Density Estimation Using Normalizing Flows

arXiv: https://arxiv.org/abs/2501.14266 · HTML: https://mlsanity.com/paper/2501.14266/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 32 of its 56 references that are in the map.
- First posted on arXiv 24 Jan 2025.

## Builds on (most cited first, 30 of 32)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
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- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [You Only Look Once: Unified, Real-Time Object Detection](https://mlsanity.com/paper/1506.02640/) (2015)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Rich feature hierarchies for accurate object detection and semantic segmentation](https://mlsanity.com/paper/1311.2524/) (2013)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Argoverse: 3D Tracking and Forecasting with Rich Maps](https://mlsanity.com/paper/1911.02620/) (2019)
- [Social GAN: Socially Acceptable Trajectories with Generative Adversarial Networks](https://mlsanity.com/paper/1803.10892/) (2018)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [Generating Sequences With Recurrent Neural Networks](https://mlsanity.com/paper/1308.0850/) (2013)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [Stable Architectures for Deep Neural Networks](https://mlsanity.com/paper/1705.03341/) (2017)
- [Beyond Finite Layer Neural Networks: Bridging Deep Architectures and Numerical Differential Equations](https://mlsanity.com/paper/1710.10121/) (2017)
- [Deep Neural Networks Motivated by Partial Differential Equations](https://mlsanity.com/paper/1804.04272/) (2018)
- [Social Attention: Modeling Attention in Human Crowds](https://mlsanity.com/paper/1710.04689/) (2017)
- [The inD Dataset: A Drone Dataset of Naturalistic Road User Trajectories at German Intersections](https://mlsanity.com/paper/1911.07602/) (2019)
- [SR-LSTM: State Refinement for LSTM towards Pedestrian Trajectory Prediction](https://mlsanity.com/paper/1903.02793/) (2019)
- [SocialVAE: Human Trajectory Prediction using Timewise Latents](https://mlsanity.com/paper/2203.08207/) (2022)
- [Occupancy Flow Fields for Motion Forecasting in Autonomous Driving](https://mlsanity.com/paper/2203.03875/) (2022)
- [FloMo: Tractable Motion Prediction with Normalizing Flows](https://mlsanity.com/paper/2103.03614/) (2021)
- [Progressive Pretext Task Learning for Human Trajectory Prediction](https://mlsanity.com/paper/2407.11588/) (2024)
- [SemanticFormer: Holistic and Semantic Traffic Scene Representation for Trajectory Prediction using Knowledge Graphs](https://mlsanity.com/paper/2404.19379/) (2024)

## Abstract (arXiv)

For intelligent transportation systems and autonomous vehicles to operate safely and efficiently, they must reliably predict the future motion and trajectory of surrounding agents within complex traffic environments. At the same time, the motion of these agents is inherently uncertain, making accurate prediction difficult. In this paper, we propose TrajFlow, a generative framework for estimating the occupancy density of dynamic agents. Our framework utilizes a causal encoder to extract semantically meaningful embeddings of the observed trajectory, as well as a normalizing flow to decode these embeddings and determine the most likely future location of an agent at some time point in the future. Our formulation differs from existing approaches because we model the marginal distribution of spatial locations instead of the joint distribution of unobserved trajectories. The advantages of a marginal formulation are numerous. First, we demonstrate that the marginal formulation produces higher accuracy on challenging trajectory forecasting benchmarks. Second, the marginal formulation allows for fully continuous sampling of future locations. Finally, marginal densities are better suited for downstream tasks as they allow for the computation of per-agent motion trajectories and occupancy grids, the two most commonly used representations for motion forecasting. We present a novel architecture based entirely on neural differential equations as an implementation of this framework and provide ablations to demonstrate the advantages of a continuous implementation over a more traditional discrete neural network based approach. The code is available at https://github.com/UMN-Choi-Lab/TrajFlow.