# FloMo: Tractable Motion Prediction with Normalizing Flows

arXiv: https://arxiv.org/abs/2103.03614 · HTML: https://mlsanity.com/paper/2103.03614/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 44 references that are in the map.
- First posted on arXiv 5 Mar 2021.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (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)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [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)
- [Social-STGCNN: A Social Spatio-Temporal Graph Convolutional Neural Network for Human Trajectory Prediction](https://mlsanity.com/paper/2002.11927/) (2020)
- [DESIRE: Distant Future Prediction in Dynamic Scenes with Interacting Agents](https://mlsanity.com/paper/1704.04394/) (2017)
- [SoPhie: An Attentive GAN for Predicting Paths Compliant to Social and Physical Constraints](https://mlsanity.com/paper/1806.01482/) (2018)
- [It Is Not the Journey but the Destination: Endpoint Conditioned Trajectory Prediction](https://mlsanity.com/paper/2004.02025/) (2020)
- [Neural Autoregressive Flows](https://mlsanity.com/paper/1804.00779/) (2018)
- [Social Attention: Modeling Attention in Human Crowds](https://mlsanity.com/paper/1710.04689/) (2017)
- [Transformer Networks for Trajectory Forecasting](https://mlsanity.com/paper/2003.08111/) (2020)
- [Mode Regularized Generative Adversarial Networks](https://mlsanity.com/paper/1612.02136/) (2016)
- [SR-LSTM: State Refinement for LSTM towards Pedestrian Trajectory Prediction](https://mlsanity.com/paper/1903.02793/) (2019)
- [Spatially-Aware Graph Neural Networks for Relational Behavior Forecasting from Sensor Data](https://mlsanity.com/paper/1910.08233/) (2019)
- [SoftFlow: Probabilistic Framework for Normalizing Flow on Manifolds](https://mlsanity.com/paper/2006.04604/) (2020)
- [What the Constant Velocity Model Can Teach Us About Pedestrian Motion Prediction](https://mlsanity.com/paper/1903.07933/) (2019)
- [Social Ways: Learning Multi-Modal Distributions of Pedestrian Trajectories with GANs](https://mlsanity.com/paper/1904.09507/) (2019)
- [FloWaveNet : A Generative Flow for Raw Audio](https://mlsanity.com/paper/1811.02155/) (2018)
- [Conditional Flow Variational Autoencoders for Structured Sequence Prediction](https://mlsanity.com/paper/1908.09008/) (2019)
- [Probabilistic Multi-modal Trajectory Prediction with Lane Attention for Autonomous Vehicles](https://mlsanity.com/paper/2007.02574/) (2020)
- [A Data-driven Model for Interaction-aware Pedestrian Motion Prediction in Object Cluttered Environments](https://mlsanity.com/paper/1709.08528/) (2017)
- [Convolutional Neural Network for Trajectory Prediction](https://mlsanity.com/paper/1809.00696/) (2018)
- [Imitative Planning using Conditional Normalizing Flow](https://mlsanity.com/paper/2007.16162/) (2020)
- [Haar Wavelet based Block Autoregressive Flows for Trajectories](https://mlsanity.com/paper/2009.09878/) (2020)

## Built on by (most cited first, 21 of 21)

- [MotionDiffuser: Controllable Multi-Agent Motion Prediction using Diffusion](https://mlsanity.com/paper/2306.03083/) (2023)
- [Fast Inference and Update of Probabilistic Density Estimation on Trajectory Prediction](https://mlsanity.com/paper/2308.08824/) (2023)
- [TrackFlow: Multi-Object Tracking with Normalizing Flows](https://mlsanity.com/paper/2308.11513/) (2023)
- [Physical Plausibility-aware Trajectory Prediction via Locomotion Embodiment](https://mlsanity.com/paper/2503.17267/) (2025)
- [Vision-based Multi-future Trajectory Prediction: A Survey](https://mlsanity.com/paper/2302.10463/) (2023)
- [Conditional Unscented Autoencoders for Trajectory Prediction](https://mlsanity.com/paper/2310.19944/) (2023)
- [Stochasticity in Motion: An Information-Theoretic Approach to Trajectory Prediction](https://mlsanity.com/paper/2410.01628/) (2024)
- [Data-Driven Stochastic Motion Evaluation and Optimization with Image by Spatially-Aligned Temporal Encoding](https://mlsanity.com/paper/2302.05041/) (2023)
- [Snapshot: Towards Application-centered Models for Pedestrian Trajectory Prediction in Urban Traffic Environments](https://mlsanity.com/paper/2409.01971/) (2024)
- [EgoCogNav: Cognition-aware Human Egocentric Navigation](https://mlsanity.com/paper/2511.17581/) (2025)
- [Generative modeling of time-dependent densities via optimal transport and projection pursuit](https://mlsanity.com/paper/2304.09663/) (2023)
- [Scene-Aware Explainable Multimodal Trajectory Prediction](https://mlsanity.com/paper/2410.16795/) (2024)
- [STEP: Structured Training and Evaluation Platform for benchmarking trajectory prediction models](https://mlsanity.com/paper/2509.14801/) (2025)
- [Reliable Probabilistic Human Trajectory Prediction for Autonomous Applications](https://mlsanity.com/paper/2410.06905/) (2024)
- [Efficient Virtuoso: A Latent Diffusion Transformer Model for Goal-Conditioned Trajectory Planning](https://mlsanity.com/paper/2509.03658/) (2025)
- [TrajFlow: A Generative Framework for Occupancy Density Estimation Using Normalizing Flows](https://mlsanity.com/paper/2501.14266/) (2025)
- [Toward Safe Integration of UAM in Terminal Airspace: UAM Route Feasibility Assessment using Probabilistic Aircraft Trajectory Prediction](https://mlsanity.com/paper/2501.16599/) (2025)
- [Selective Social-Interaction via Individual Importance for Fast Human Trajectory Prediction](https://mlsanity.com/paper/2506.18291/) (2025)
- [Muninn: Your Trajectory Diffusion Model But Faster](https://mlsanity.com/paper/2605.09999/) (2026)
- [Hybrid Probabilistic Zonotopes for Identifiable and Refinable Predictive Uncertainty](https://mlsanity.com/paper/2608.05454/) (2026)
- [Gaussian-Mixture Latent Flow for Stochastic 3D Human Motion Prediction](https://mlsanity.com/paper/2608.21093/) (2026)

## Abstract (arXiv)

The future motion of traffic participants is inherently uncertain. To plan safely, therefore, an autonomous agent must take into account multiple possible trajectory outcomes and prioritize them. Recently, this problem has been addressed with generative neural networks. However, most generative models either do not learn the true underlying trajectory distribution reliably, or do not allow predictions to be associated with likelihoods. In our work, we model motion prediction directly as a density estimation problem with a normalizing flow between a noise distribution and the future motion distribution. Our model, named FloMo, allows likelihoods to be computed in a single network pass and can be trained directly with maximum likelihood estimation. Furthermore, we propose a method to stabilize training flows on trajectory datasets and a new data augmentation transformation that improves the performance and generalization of our model. Our method achieves state-of-the-art performance on three popular prediction datasets, with a significant gap to most competing models.