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DD-MDN: Human Trajectory Forecasting with Diffusion-Based Dual Mixture Density Networks and Uncertainty Self-Calibration

Manuel Hetzel, Kerim Turacan, Hannes Reichert, Konrad Doll, Bernhard Sick

TL;DR

This paper tackles uncertainty calibration and short-observation robustness in human trajectory forecasting by introducing DD-MDN, a diffusion-based dual-MDN framework. It integrates a few-shot denoising diffusion backbone with two Gaussian-mixture heads to produce per-timestep and per-anchor-trajectory distributions, enabling calibrated, multimodal forecasts without predefined endpoints. The model achieves state-of-the-art accuracy and reliable uncertainty estimates across ETH/UCY, SDD, inD, and IMPTC, and shows strong performance under short observation intervals. The unsupervised diffusion prior provides global coherence in the parameter space, improving calibration and stability, with practical implications for planning and collision avoidance in autonomous systems.

Abstract

Human Trajectory Forecasting (HTF) predicts future human movements from past trajectories and environmental context, with applications in Autonomous Driving, Smart Surveillance, and Human-Robot Interaction. While prior work has focused on accuracy, social interaction modeling, and diversity, little attention has been paid to uncertainty modeling, calibration, and forecasts from short observation periods, which are crucial for downstream tasks such as path planning and collision avoidance. We propose DD-MDN, an end-to-end probabilistic HTF model that combines high positional accuracy, calibrated uncertainty, and robustness to short observations. Using a few-shot denoising diffusion backbone and a dual mixture density network, our method learns self-calibrated residence areas and probability-ranked anchor paths, from which diverse trajectory hypotheses are derived, without predefined anchors or endpoints. Experiments on the ETH/UCY, SDD, inD, and IMPTC datasets demonstrate state-of-the-art accuracy, robustness at short observation intervals, and reliable uncertainty modeling. The code is available at: https://github.com/kav-institute/ddmdn.

DD-MDN: Human Trajectory Forecasting with Diffusion-Based Dual Mixture Density Networks and Uncertainty Self-Calibration

TL;DR

This paper tackles uncertainty calibration and short-observation robustness in human trajectory forecasting by introducing DD-MDN, a diffusion-based dual-MDN framework. It integrates a few-shot denoising diffusion backbone with two Gaussian-mixture heads to produce per-timestep and per-anchor-trajectory distributions, enabling calibrated, multimodal forecasts without predefined endpoints. The model achieves state-of-the-art accuracy and reliable uncertainty estimates across ETH/UCY, SDD, inD, and IMPTC, and shows strong performance under short observation intervals. The unsupervised diffusion prior provides global coherence in the parameter space, improving calibration and stability, with practical implications for planning and collision avoidance in autonomous systems.

Abstract

Human Trajectory Forecasting (HTF) predicts future human movements from past trajectories and environmental context, with applications in Autonomous Driving, Smart Surveillance, and Human-Robot Interaction. While prior work has focused on accuracy, social interaction modeling, and diversity, little attention has been paid to uncertainty modeling, calibration, and forecasts from short observation periods, which are crucial for downstream tasks such as path planning and collision avoidance. We propose DD-MDN, an end-to-end probabilistic HTF model that combines high positional accuracy, calibrated uncertainty, and robustness to short observations. Using a few-shot denoising diffusion backbone and a dual mixture density network, our method learns self-calibrated residence areas and probability-ranked anchor paths, from which diverse trajectory hypotheses are derived, without predefined anchors or endpoints. Experiments on the ETH/UCY, SDD, inD, and IMPTC datasets demonstrate state-of-the-art accuracy, robustness at short observation intervals, and reliable uncertainty modeling. The code is available at: https://github.com/kav-institute/ddmdn.
Paper Structure (18 sections, 22 equations, 5 figures, 4 tables)

This paper contains 18 sections, 22 equations, 5 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Deterministic Methods
  4. Probabilistic Methods and Uncertainty Modeling
  5. Contributions
  6. Methodology
  7. Problem Statement
  8. Architecture
  9. Input Encoding
  10. Probabilistic Modeling
  11. Unsupervised Transformer Diffusion
  12. Deterministic Hypotheses Generation
  13. Training Details
  14. Experiments
  15. Experimental Setup
  16. ...and 3 more sections

Figures (5)

  • Figure 1: Architectural overview of DD-MDN. Input encoding blocks are green, probabilistic blocks are yellow, and deterministic ones are blue.
  • Figure 2: Internal GM representations, f.l.t.r.: First: Per-timestep GM representation in $\mathbb{R}^2$ space as 95- and 68 % mixture CLs. Second: Per-anchor-trajectory GM representation in $\mathbb{R}^{2T_{fut}}$ trajectory space visualized by three anchor trajectories and their uncertainties. Third: Final discrete $K$ generated hypotheses. GT path is red.
  • Figure 3: Schematic illustration of the two GM types, f.l.t.r.: First: Uncorrelated Gaussian parameters per-timestep (gray). Second: Representation in $\mathbb{R}^2$ space. Third: per-anchor-trajectory GM representation in $\mathbb{R}^{2T_{fut}}$ trajectory space.
  • Figure 4: DD-MDN results in various datasets, f.l.t.r.: (1) IMPTC per-anchor-trajectory GM representation and (2) resulting final $K$ hypotheses with 68- and 95 % CLs, (3-5) inD, SDD, and ETH examples, (6) IMPTC- and (7) inD per-timestep 68- and 95 % isolated CL forecasts.
  • Figure 5: Upper Row: Calibration plots of SOTA methods (LED, SingularTraj) and DD-MDN for ETH/UCY Zara01 benchmark. Lower Row: Calibration plots for the SDD*, IMPTC* and inD*full datasets. Colors represent future timesteps (0.8, 1.6, ..., 4.8 s), the black dotted diagonal represents perfect calibration.