# Unified Uncertainty-Aware Diffusion for Multi-Agent Trajectory Modeling

arXiv: https://arxiv.org/abs/2503.18589 · HTML: https://mlsanity.com/paper/2503.18589/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 55 of its 68 references that are in the map.
- First posted on arXiv 24 Mar 2025.

## Builds on (most cited first, 30 of 55)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Social GAN: Socially Acceptable Trajectories with Generative Adversarial Networks](https://mlsanity.com/paper/1803.10892/) (2018)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [MultiPath: Multiple Probabilistic Anchor Trajectory Hypotheses for Behavior Prediction](https://mlsanity.com/paper/1910.05449/) (2019)
- [TNT: Target-driveN Trajectory Prediction](https://mlsanity.com/paper/2008.08294/) (2020)
- [On human motion prediction using recurrent neural networks](https://mlsanity.com/paper/1705.02445/) (2017)
- [AgentFormer: Agent-Aware Transformers for Socio-Temporal Multi-Agent Forecasting](https://mlsanity.com/paper/2103.14023/) (2021)
- [SoPhie: An Attentive GAN for Predicting Paths Compliant to Social and Physical Constraints](https://mlsanity.com/paper/1806.01482/) (2018)
- [CoverNet: Multimodal Behavior Prediction using Trajectory Sets](https://mlsanity.com/paper/1911.10298/) (2019)
- [Learning Trajectory Dependencies for Human Motion Prediction](https://mlsanity.com/paper/1908.05436/) (2019)
- [It Is Not the Journey but the Destination: Endpoint Conditioned Trajectory Prediction](https://mlsanity.com/paper/2004.02025/) (2020)
- [Structural-RNN: Deep Learning on Spatio-Temporal Graphs](https://mlsanity.com/paper/1511.05298/) (2015)
- [Social-BiGAT: Multimodal Trajectory Forecasting using Bicycle-GAN and Graph Attention Networks](https://mlsanity.com/paper/1907.03395/) (2019)
- [MotionDiffuser: Controllable Multi-Agent Motion Prediction using Diffusion](https://mlsanity.com/paper/2306.03083/) (2023)
- [Diffusion-based Time Series Imputation and Forecasting with Structured State Space Models](https://mlsanity.com/paper/2208.09399/) (2022)
- [Fast Differentiable Sorting and Ranking](https://mlsanity.com/paper/2002.08871/) (2020)
- [Stochastic Trajectory Prediction via Motion Indeterminacy Diffusion](https://mlsanity.com/paper/2203.13777/) (2022)
- [History Repeats Itself: Human Motion Prediction via Motion Attention](https://mlsanity.com/paper/2007.11755/) (2020)
- [Scene Transformer: A unified architecture for predicting multiple agent trajectories](https://mlsanity.com/paper/2106.08417/) (2021)
- [Trace and Pace: Controllable Pedestrian Animation via Guided Trajectory Diffusion](https://mlsanity.com/paper/2304.01893/) (2023)
- [A Spatio-temporal Transformer for 3D Human Motion Prediction](https://mlsanity.com/paper/2004.08692/) (2020)
- [Leapfrog Diffusion Model for Stochastic Trajectory Prediction](https://mlsanity.com/paper/2303.10895/) (2023)
- [Latent Variable Sequential Set Transformers For Joint Multi-Agent Motion Prediction](https://mlsanity.com/paper/2104.00563/) (2021)
- [GroupNet: Multiscale Hypergraph Neural Networks for Trajectory Prediction with Relational Reasoning](https://mlsanity.com/paper/2204.08770/) (2022)
- [Back to MLP: A Simple Baseline for Human Motion Prediction](https://mlsanity.com/paper/2207.01567/) (2022)

## Built on by (most cited first, 15 of 15)

- [JointDiff: Bridging Continuous and Discrete in Multi-Agent Trajectory Generation](https://mlsanity.com/paper/2509.22522/) (2025)
- [SoccerNet-v3D: Leveraging Sports Broadcast Replays for 3D Scene Understanding](https://mlsanity.com/paper/2504.10106/) (2025)
- [Flow Matching with Uncertainty Quantification and Guidance](https://mlsanity.com/paper/2602.10326/) (2026)
- [Heteroscedastic Diffusion for Multi-Agent Trajectory Modeling](https://mlsanity.com/paper/2605.10717/) (2026)
- [Improved Constrained Generation by Bridging Pretrained Generative Models](https://mlsanity.com/paper/2603.06742/) (2026)
- [Multi-Modal Soccer Scene Analysis with Masked Pre-Training](https://mlsanity.com/paper/2512.19528/) (2025)
- [Modeling Matches as Language: A Generative Transformer Approach for Counterfactual Player Valuation in Football](https://mlsanity.com/paper/2603.15212/) (2026)
- [Social-Mamba: Socially-Aware Trajectory Forecasting with State-Space Models](https://mlsanity.com/paper/2605.15424/) (2026)
- [MUMINS: Metadata-conditioned Uncertainty-aware Medical Image Next-state Synthesis](https://mlsanity.com/paper/2609.17169/) (2026)
- [AdaSports-Traj: Role- and Domain-Aware Adaptation for Multi-Agent Trajectory Modeling in Sports](https://mlsanity.com/paper/2509.16095/) (2025)
- [PathCRF: Ball-Free Soccer Event Detection via Possession Path Inference from Player Trajectories](https://mlsanity.com/paper/2602.12080/) (2026)
- [JACoP: Joint Alignment for Compliant Multi-Agent Prediction](https://mlsanity.com/paper/2605.11385/) (2026)
- [SSP-DMGTimeNet: Physics-Constrained Learning for Spatiotemporal Trajectory Prediction of Vehicle Platoons](https://mlsanity.com/paper/2609.06961/) (2026)
- [HAP: A Hand-Driven Active Perception Framework for Egocentric Head Motion Prediction](https://mlsanity.com/paper/2609.18548/) (2026)
- [Is your uncertainty map wrong, or is its target? Exact diagnostics for the Tweedie diagonal, and a gradient-free alternative](https://mlsanity.com/paper/2609.33786/) (2026)

## Abstract (arXiv)

Multi-agent trajectory modeling has primarily focused on forecasting future states, often overlooking broader tasks like trajectory completion, which are crucial for real-world applications such as correcting tracking data. Existing methods also generally predict agents' states without offering any state-wise measure of uncertainty. Moreover, popular multi-modal sampling methods lack any error probability estimates for each generated scene under the same prior observations, making it difficult to rank the predictions during inference time. We introduce U2Diff, a unified diffusion model designed to handle trajectory completion while providing state-wise uncertainty estimates jointly. This uncertainty estimation is achieved by augmenting the simple denoising loss with the negative log-likelihood of the predicted noise and propagating latent space uncertainty to the real state space. Additionally, we incorporate a Rank Neural Network in post-processing to enable error probability estimation for each generated mode, demonstrating a strong correlation with the error relative to ground truth. Our method outperforms the state-of-the-art solutions in trajectory completion and forecasting across four challenging sports datasets (NBA, Basketball-U, Football-U, Soccer-U), highlighting the effectiveness of uncertainty and error probability estimation. Video at https://youtu.be/ngw4D4eJToE