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SingularTrajectory: Universal Trajectory Predictor Using Diffusion Model
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Proposes SingularTrajectory, a diffusion-based universal trajectory predictor that projects motion from all five trajectory prediction tasks into an SVD-derived Singular space and refines traversability-adapted anchors with a diffusion model.
Problem
Trajectory prediction is split into five task variants (stochastic, deterministic, momentary observation, domain adaptation, few-shot), each typically requiring specialized architectures, and models suffer large performance drops when transferred across tasks.
Approach
Build a shared Singular space from truncated SVD of motion data (with B-spline interpolation for variable lengths), deform fixed prototype anchors with a vector field from a traversability map, and refine the anchors via a cascaded diffusion model that predicts residuals.
Key results
- Stochastic prediction on ETH-UCY averages 0.21/0.32 ADE/FDE (20 samples), competitive with top methods such as NPSN and EqMotion.
- Deterministic prediction averages 0.47/0.90 ADE/FDE, best among compared methods in Table 3.
- Domain adaptation averages 0.48 ADE and momentary observation averages 0.25/0.40, with few-shot at 0.23/0.35.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use SingularTrajectory instead of SocialVAE | Stochastic ETH-UCY prediction · ETH-UCY AVG | ADE/FDE: 0.21/0.33 -> 0.21/0.32 | Mixed |
| Use SingularTrajectory instead of Trajectron++ | Deterministic ETH-UCY prediction · ETH-UCY AVG | ADE/FDE: 0.52/1.11 -> 0.47/0.90 | Helped |
| Use SingularTrajectory instead of EigenTrajectory | Momentary ETH-UCY prediction · ETH-UCY AVG | ADE/FDE: 0.25/0.42 -> 0.25/0.40 | Mixed |
| Use SingularTrajectory instead of Adaptive | Domain adaptation · ETH-UCY AVG | ADE: 0.59 -> 0.48 | Helped |
| Use SingularTrajectory instead of Adaptive | Domain adaptation · ETH-UCY AVG | FDE: 1.22 -> 0.94 | Helped |
| Use SingularTrajectory instead of EigenTrajectory | Few-shot ETH-UCY prediction · ETH-UCY AVG | ADE/FDE: 0.23/0.39 -> 0.23/0.35 | Mixed |
| Use K=4 rather than K=1 motion vectors (ablation) | SingularTrajectory · ZARA1 all tasks average | ADE/FDE: 0.40 / 0.77 -> 0.30 / 0.59 | Helped |
| Set Singular space dimension to K=5 or K=6 rather than K=4 (ablation) | SingularTrajectory · ZARA1 all tasks average | ADE/FDE: 0.30 / 0.59 -> 0.30 / 0.60 | Mixed |
| Denoise directly from Gaussian noise instead of refining a prototype anchor (ablation) | SingularTrajectory · All five tasks | ADE/FDE: 0.30 / 0.59 -> 0.48 / 0.91 | Hurt |
| Use the anchor as an intermediate state without residual denoising (ablation) | SingularTrajectory · All five tasks | ADE/FDE: 0.30 / 0.59 -> 0.33 / 0.66 | Hurt |
| Refine prototype paths independently instead of jointly (ablation) | SingularTrajectory · All five tasks | ADE/FDE: 0.30 / 0.59 -> 0.32 / 0.65 | Hurt |
| Use M=1, 2, or 5 diffusion steps instead of M=10 (ablation) | SingularTrajectory · All five tasks | ADE/FDE: M=1: 0.31 / 0.61; M=2: 0.30 / 0.60; M=5: 0.30 / 0.60; M=10: 0.30 / 0.59 | Mixed |
Surprising findings
- Denoising a residual over an adaptive anchor works better than denoising from pure Gaussian noise (MID-style), which scored worst in ablation (average 0.48/0.91 vs 0.30/0.59).
Limitations
- Relies on an off-the-shelf semantic segmentation model to produce traversability maps for anchor adaptation.
- Performance on some stochastic scenes (e.g., ETH ADE/FDE 0.35/0.42) is not best and the stochastic average is only competitive, not state-of-the-art.
Experimental setup
Datasets: ETH UCY
Benchmarks: ETH UCY HOTEL UNIV ZARA1 ZARA2
Metrics: ADE FDE
Baselines: EigenTrajectory MID AgentFormer PECNet STGCNN LED T-GNN Adaptive [24] MOE-Traj++
Builds on: EigenTrajectory MID LED DDIM
Closest papers by meaning
- Optimizing Diffusion Noise Can Serve As Universal Motion Priors (CVPR 2024 · similarity 0.86)
- Human Motion Diffusion as a Generative Prior (ICLR 2024 · similarity 0.86)
- Social-Transmotion: Promptable Human Trajectory Prediction (ICLR 2024 · similarity 0.86)
- Homogeneous Dynamics Space for Heterogeneous Humans (CVPR 2025 · similarity 0.86)
- ProDiff: Prototype-Guided Diffusion for Minimal Information Trajectory Imputation (ICML 2025 · similarity 0.86)
- Physical Plausibility-aware Trajectory Prediction via Locomotion Embodiment (CVPR 2025 · similarity 0.86)
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