# MUSE-VAE: Multi-Scale VAE for Environment-Aware Long Term Trajectory Prediction

arXiv: https://arxiv.org/abs/2201.07189 · HTML: https://mlsanity.com/paper/2201.07189/

## Key facts

- Cited by 59 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 50 references that are in the map.
- First posted on arXiv 18 Jan 2022.

## Builds on (most cited first, 25 of 25)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [nuScenes: A multimodal dataset for autonomous driving](https://mlsanity.com/paper/1903.11027/) (2019)
- [A large annotated corpus for learning natural language inference](https://mlsanity.com/paper/1508.05326/) (2015)
- [Focal Loss for Dense Object Detection](https://mlsanity.com/paper/1708.02002/) (2017)
- [Social GAN: Socially Acceptable Trajectories with Generative Adversarial Networks](https://mlsanity.com/paper/1803.10892/) (2018)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [Generating Sentences from a Continuous Space](https://mlsanity.com/paper/1511.06349/) (2015)
- [TNT: Target-driveN Trajectory Prediction](https://mlsanity.com/paper/2008.08294/) (2020)
- [AgentFormer: Agent-Aware Transformers for Socio-Temporal Multi-Agent Forecasting](https://mlsanity.com/paper/2103.14023/) (2021)
- [Ladder Variational Autoencoders](https://mlsanity.com/paper/1602.02282/) (2016)
- [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)
- [A Probabilistic U-Net for Segmentation of Ambiguous Images](https://mlsanity.com/paper/1806.05034/) (2018)
- [CoverNet: Multimodal Behavior Prediction using Trajectory Sets](https://mlsanity.com/paper/1911.10298/) (2019)
- [Social-BiGAT: Multimodal Trajectory Forecasting using Bicycle-GAN and Graph Attention Networks](https://mlsanity.com/paper/1907.03395/) (2019)
- [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)
- [PRECOG: PREdiction Conditioned On Goals in Visual Multi-Agent Settings](https://mlsanity.com/paper/1905.01296/) (2019)
- [Multiple Futures Prediction](https://mlsanity.com/paper/1911.00997/) (2019)
- [From Goals, Waypoints & Paths To Long Term Human Trajectory Forecasting](https://mlsanity.com/paper/2012.01526/) (2020)
- [Time for a change: a tutorial for comparing multiple classifiers through Bayesian analysis](https://mlsanity.com/paper/1606.04316/) (2016)
- [Stepwise Goal-Driven Networks for Trajectory Prediction](https://mlsanity.com/paper/2103.14107/) (2021)
- [A Surprisingly Effective Fix for Deep Latent Variable Modeling of Text](https://mlsanity.com/paper/1909.00868/) (2019)

## Built on by (most cited first, 30 of 59)

- [Leapfrog Diffusion Model for Stochastic Trajectory Prediction](https://mlsanity.com/paper/2303.10895/) (2023)
- [Learning Pedestrian Group Representations for Multi-modal Trajectory Prediction](https://mlsanity.com/paper/2207.09953/) (2022)
- [EigenTrajectory: Low-Rank Descriptors for Multi-Modal Trajectory Forecasting](https://mlsanity.com/paper/2307.09306/) (2023)
- [SingularTrajectory: Universal Trajectory Predictor Using Diffusion Model](https://mlsanity.com/paper/2403.18452/) (2024)
- [FEND: A Future Enhanced Distribution-Aware Contrastive Learning Framework for Long-tail Trajectory Prediction](https://mlsanity.com/paper/2303.16574/) (2023)
- [Can Language Beat Numerical Regression? Language-Based Multimodal Trajectory Prediction](https://mlsanity.com/paper/2403.18447/) (2024)
- [MoFlow: One-Step Flow Matching for Human Trajectory Forecasting via Implicit Maximum Likelihood Estimation based Distillation](https://mlsanity.com/paper/2503.09950/) (2025)
- [Multi-agent Long-term 3D Human Pose Forecasting via Interaction-aware Trajectory Conditioning](https://mlsanity.com/paper/2404.05218/) (2024)
- [SocialCircle: Learning the Angle-based Social Interaction Representation for Pedestrian Trajectory Prediction](https://mlsanity.com/paper/2310.05370/) (2023)
- [GATraj: A Graph- and Attention-based Multi-Agent Trajectory Prediction Model](https://mlsanity.com/paper/2209.07857/) (2022)
- [LG-Traj: LLM Guided Pedestrian Trajectory Prediction](https://mlsanity.com/paper/2403.08032/) (2024)
- [MART: MultiscAle Relational Transformer Networks for Multi-agent Trajectory Prediction](https://mlsanity.com/paper/2407.21635/) (2024)
- [T4P: Test-Time Training of Trajectory Prediction via Masked Autoencoder and Actor-specific Token Memory](https://mlsanity.com/paper/2403.10052/) (2024)
- [Unsupervised Sampling Promoting for Stochastic Human Trajectory Prediction](https://mlsanity.com/paper/2304.04298/) (2023)
- [Progressive Pretext Task Learning for Human Trajectory Prediction](https://mlsanity.com/paper/2407.11588/) (2024)
- [Unified Uncertainty-Aware Diffusion for Multi-Agent Trajectory Modeling](https://mlsanity.com/paper/2503.18589/) (2025)
- [Trajectory Prediction for Autonomous Driving: Progress, Limitations, and Future Directions](https://mlsanity.com/paper/2503.03262/) (2025)
- [Improving Transferability for Cross-domain Trajectory Prediction via Neural Stochastic Differential Equation](https://mlsanity.com/paper/2312.15906/) (2023)
- [SocialCVAE: Predicting Pedestrian Trajectory via Interaction Conditioned Latents](https://mlsanity.com/paper/2402.17339/) (2024)
- [Curb Your Attention: Causal Attention Gating for Robust Trajectory Prediction in Autonomous Driving](https://mlsanity.com/paper/2410.07191/) (2024)
- [Pedestrian Trajectory Prediction with Missing Data: Datasets, Imputation, and Benchmarking](https://mlsanity.com/paper/2411.00174/) (2024)
- [TrajFlow: Multi-modal Motion Prediction via Flow Matching](https://mlsanity.com/paper/2506.08541/) (2025)
- [Conditional Unscented Autoencoders for Trajectory Prediction](https://mlsanity.com/paper/2310.19944/) (2023)
- [TrACT: A Training Dynamics Aware Contrastive Learning Framework for Long-tail Trajectory Prediction](https://mlsanity.com/paper/2404.12538/) (2024)
- [SocialCircle+: Learning the Angle-based Conditioned Interaction Representation for Pedestrian Trajectory Prediction](https://mlsanity.com/paper/2409.14984/) (2024)
- [Continuous Locomotive Crowd Behavior Generation](https://mlsanity.com/paper/2504.04756/) (2025)
- [Staged Contact-Aware Global Human Motion Forecasting](https://mlsanity.com/paper/2309.08947/) (2023)
- [DESTINE: Dynamic Goal Queries with Temporal Transductive Alignment for Trajectory Prediction](https://mlsanity.com/paper/2310.07438/) (2023)
- [Resonance: Learning to Predict Social-Aware Pedestrian Trajectories as Co-Vibrations](https://mlsanity.com/paper/2412.02447/) (2024)
- [JointDiff: Bridging Continuous and Discrete in Multi-Agent Trajectory Generation](https://mlsanity.com/paper/2509.22522/) (2025)

## Abstract (arXiv)

Accurate long-term trajectory prediction in complex scenes, where multiple agents (e.g., pedestrians or vehicles) interact with each other and the environment while attempting to accomplish diverse and often unknown goals, is a challenging stochastic forecasting problem. In this work, we propose MUSE, a new probabilistic modeling framework based on a cascade of Conditional VAEs, which tackles the long-term, uncertain trajectory prediction task using a coarse-to-fine multi-factor forecasting architecture. In its Macro stage, the model learns a joint pixel-space representation of two key factors, the underlying environment and the agent movements, to predict the long and short-term motion goals. Conditioned on them, the Micro stage learns a fine-grained spatio-temporal representation for the prediction of individual agent trajectories. The VAE backbones across the two stages make it possible to naturally account for the joint uncertainty at both levels of granularity. As a result, MUSE offers diverse and simultaneously more accurate predictions compared to the current state-of-the-art. We demonstrate these assertions through a comprehensive set of experiments on nuScenes and SDD benchmarks as well as PFSD, a new synthetic dataset, which challenges the forecasting ability of models on complex agent-environment interaction scenarios.