# MGF: Mixed Gaussian Flow for Diverse Trajectory Prediction

arXiv: https://arxiv.org/abs/2402.12238 · HTML: https://mlsanity.com/paper/2402.12238/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 65 references that are in the map.
- First posted on arXiv 19 Feb 2024.

## Builds on (most cited first, 30 of 42)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Social GAN: Socially Acceptable Trajectories with Generative Adversarial Networks](https://mlsanity.com/paper/1803.10892/) (2018)
- [AgentFormer: Agent-Aware Transformers for Socio-Temporal Multi-Agent Forecasting](https://mlsanity.com/paper/2103.14023/) (2021)
- [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)
- [Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Models](https://mlsanity.com/paper/2103.04922/) (2021)
- [It Is Not the Journey but the Destination: Endpoint Conditioned Trajectory Prediction](https://mlsanity.com/paper/2004.02025/) (2020)
- [Why Normalizing Flows Fail to Detect Out-of-Distribution Data](https://mlsanity.com/paper/2006.08545/) (2020)
- [Deep Unsupervised Clustering with Gaussian Mixture Variational Autoencoders](https://mlsanity.com/paper/1611.02648/) (2016)
- [Spatio-Temporal Graph Transformer Networks for Pedestrian Trajectory Prediction](https://mlsanity.com/paper/2005.08514/) (2020)
- [Social Attention: Modeling Attention in Human Crowds](https://mlsanity.com/paper/1710.04689/) (2017)
- [DLow: Diversifying Latent Flows for Diverse Human Motion Prediction](https://mlsanity.com/paper/2003.08386/) (2020)
- [Stochastic Trajectory Prediction via Motion Indeterminacy Diffusion](https://mlsanity.com/paper/2203.13777/) (2022)
- [PRECOG: PREdiction Conditioned On Goals in Visual Multi-Agent Settings](https://mlsanity.com/paper/1905.01296/) (2019)
- [From Goals, Waypoints & Paths To Long Term Human Trajectory Forecasting](https://mlsanity.com/paper/2012.01526/) (2020)
- [Leapfrog Diffusion Model for Stochastic Trajectory Prediction](https://mlsanity.com/paper/2303.10895/) (2023)
- [GroupNet: Multiscale Hypergraph Neural Networks for Trajectory Prediction with Relational Reasoning](https://mlsanity.com/paper/2204.08770/) (2022)
- [Peeking into the Future: Predicting Future Person Activities and Locations in Videos](https://mlsanity.com/paper/1902.03748/) (2019)
- [SR-LSTM: State Refinement for LSTM towards Pedestrian Trajectory Prediction](https://mlsanity.com/paper/1903.02793/) (2019)
- [EqMotion: Equivariant Multi-agent Motion Prediction with Invariant Interaction Reasoning](https://mlsanity.com/paper/2303.10876/) (2023)
- [Remember Intentions: Retrospective-Memory-based Trajectory Prediction](https://mlsanity.com/paper/2203.11474/) (2022)
- [Semi-Supervised Learning with Normalizing Flows](https://mlsanity.com/paper/1912.13025/) (2019)
- [Diverse and Admissible Trajectory Forecasting through Multimodal Context Understanding](https://mlsanity.com/paper/2003.03212/) (2020)
- [MG-GAN: A Multi-Generator Model Preventing Out-of-Distribution Samples in Pedestrian Trajectory Prediction](https://mlsanity.com/paper/2108.09274/) (2021)
- [Three Steps to Multimodal Trajectory Prediction: Modality Clustering, Classification and Synthesis](https://mlsanity.com/paper/2103.07854/) (2021)
- [Social-Implicit: Rethinking Trajectory Prediction Evaluation and The Effectiveness of Implicit Maximum Likelihood Estimation](https://mlsanity.com/paper/2203.03057/) (2022)
- [RAIN: Reinforced Hybrid Attention Inference Network for Motion Forecasting](https://mlsanity.com/paper/2108.01316/) (2021)

## Built on by (most cited first, 6 of 6)

- [FollowGen: A Scaled Noise Conditional Diffusion Model for Car-Following Trajectory Prediction](https://mlsanity.com/paper/2411.16747/) (2024)
- [RealTraj: Towards Real-World Pedestrian Trajectory Forecasting](https://mlsanity.com/paper/2411.17376/) (2024)
- [Crossfusor: A Cross-Attention Transformer Enhanced Conditional Diffusion Model for Car-Following Trajectory Prediction](https://mlsanity.com/paper/2406.11941/) (2024)
- [Towards Efficient Real-Time Video Motion Transfer via Generative Time Series Modeling](https://mlsanity.com/paper/2504.05537/) (2025)
- [Recent Advances in Multi-Agent Human Trajectory Prediction: A Comprehensive Review](https://mlsanity.com/paper/2506.14831/) (2025)
- [PatchTraj: Unified Time-Frequency Representation Learning via Dynamic Patches for Trajectory Prediction](https://mlsanity.com/paper/2507.19119/) (2025)

## Abstract (arXiv)

To predict future trajectories, the normalizing flow with a standard Gaussian prior suffers from weak diversity. The ineffectiveness comes from the conflict between the fact of asymmetric and multi-modal distribution of likely outcomes and symmetric and single-modal original distribution and supervision losses. Instead, we propose constructing a mixed Gaussian prior for a normalizing flow model for trajectory prediction. The prior is constructed by analyzing the trajectory patterns in the training samples without requiring extra annotations while showing better expressiveness and being multi-modal and asymmetric. Besides diversity, it also provides better controllability for probabilistic trajectory generation. We name our method Mixed Gaussian Flow (MGF). It achieves state-of-the-art performance in the evaluation of both trajectory alignment and diversity on the popular UCY/ETH and SDD datasets. Code is available at https://github.com/mulplue/MGF.