Heteroscedastic Diffusion for Multi-Agent Trajectory Modeling

2026-05-11

AI Summary

This work addresses the limitations of existing methods in multi-agent trajectory modeling, which struggle to support trajectory completion and lack joint estimation of state-level heteroscedastic uncertainty and error probabilities of generated samples. To overcome these challenges, the authors propose U2Diffine, a unified diffusion model that enables both trajectory completion and state-level uncertainty quantification through an enhanced denoising loss and first-order Taylor expansion. Furthermore, they introduce U2Diff, a gradient-free fast sampling variant, along with RankNN, a post-processing network that ranks error probabilities of generated modes, thereby enabling efficient inference. This approach is the first to jointly achieve these three capabilities in multi-agent trajectory tasks and demonstrates significant performance gains over state-of-the-art methods on the NBA, Basketball-U, Football-U, and Soccer-U datasets, validating its effectiveness and practicality.

Abstract

Multi-agent trajectory modeling traditionally focuses on forecasting, often neglecting more general tasks like trajectory completion, which is essential for real-world applications such as correcting tracking data. Existing methods also generally predict agents' states without offering any state-wise measure of heteroscedastic uncertainty. Moreover, popular multi-modal sampling methods lack error probability estimates for each generated scene under the same prior observations, which makes it difficult to rank the predictions at inference time. We introduce U2Diffine, a unified diffusion model built to perform trajectory completion while simultaneously offering state-wise heteroscedastic uncertainty estimates. This is achieved by augmenting the standard denoising loss with the negative log-likelihood of the predicted noise, and then propagating the latent space uncertainty to the real state space using a first-order Taylor approximation. We also propose U2Diff, a faster baseline that avoids gradient computation during sampling. This approach significantly increases inference speed, making it as efficient as a standard generative-only diffusion model. For post-processing, we integrate a Rank Neural Network (RankNN) that enables error probability estimation for each generated mode, demonstrating strong correlation with ground truth errors. Our method outperforms state-of-the-art solutions in both trajectory completion and forecasting across four challenging sports datasets (NBA, Basketball-U, Football-U, Soccer-U), underscoring the effectiveness of our uncertainty and error probability estimation.

Problem

• multi-agent trajectory modeling
• trajectory completion
• heteroscedastic uncertainty
• error probability estimation
• multi-modal sampling

Innovation

• heteroscedastic diffusion
• trajectory completion
• uncertainty estimation
• multi-agent trajectory modeling
• Rank Neural Network