# Heteroscedastic Diffusion for Multi-Agent Trajectory Modeling

arXiv: https://arxiv.org/abs/2605.10717 · HTML: https://mlsanity.com/paper/2605.10717/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion and flow policies for robotics, one of 14 directions in Diffusion models.
- Builds on 65 of its 88 references that are in the map.
- First posted on arXiv 11 May 2026.

## Placed in

- Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/)

## Builds on (most cited first, 30 of 65)

- [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)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (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)
- [Motion Transformer with Global Intention Localization and Local Movement Refinement](https://mlsanity.com/paper/2209.13508/) (2022)
- [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)

## Built on by (most cited first, 3 of 3)

- [MUMINS: Metadata-conditioned Uncertainty-aware Medical Image Next-state Synthesis](https://mlsanity.com/paper/2609.17169/) (2026)
- [Testing and Evaluation of Agentic AI Systems In Military Command and Control](https://mlsanity.com/paper/2608.20597/) (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 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.