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STGDPM:Vessel Trajectory Prediction with Spatio-Temporal Graph Diffusion Probabilistic Model

The paper proposes STGDPM, a novel Spatio-Temporal Graph Diffusion Probabilistic Model that integrates dynamic graph-based interaction modeling with diffusion processes to effectively capture multimodal vessel behaviors and improve trajectory prediction accuracy in maritime safety.

Original authors: Jin Wenzhe, Tang Haina, Zhang Xudong

Published 2026-08-04

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Jin Wenzhe, Tang Haina, Zhang Xudong

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are standing on a busy highway, watching cars zip by. If you wanted to guess where a specific car will be in ten seconds, you might look at its speed and direction. But real life is messy. That car might suddenly swerve to avoid a pothole, slow down for a red light, or merge because the car next to it is moving too fast. Predicting the future of moving things is a huge puzzle for scientists, especially when those things are giant ships on the ocean. This field of study is called trajectory prediction. It's all about using math and computers to guess where something will go next. To do this well, computers need to understand two tricky things: interaction (how objects affect each other, like ships avoiding collisions) and multi-modality (the idea that there isn't just one "right" future, but several possible ones, like a ship could turn left, turn right, or keep going straight). If we get this wrong, ships could crash, causing damage and danger. So, scientists are always looking for smarter ways to solve this puzzle.

Enter a new team of researchers who decided to tackle this problem with a fresh, almost magical approach. They noticed that old methods were like trying to guess a ship's path by just averaging out the movements of nearby boats, which often missed the subtle, complex dance of the ocean. Instead, they built a system called STGDPM. Think of it as a "time-reversal magic trick" combined with a dynamic map.

Here is how their invention works, using a simple analogy. Imagine a ship's future path is a clear, straight line drawn on a piece of paper. Now, imagine someone starts shaking the paper violently, adding static noise until the line is completely invisible and just looks like a blurry mess of gray fuzz. This is what the researchers call the "diffusion" process—turning a clear answer into total chaos.

The old way of predicting paths was like trying to guess the original line just by looking at the blurry mess and hoping for the best. But this new system, STGDPM, is like a super-smart detective who has seen the blurry mess and knows exactly what the clear line looked like before the shaking started. It uses a special tool called a Denoising Network (which they named Traj-UGnet) to slowly, step-by-step, remove the "noise" from the blurry mess. As it removes the fuzz, the clear path of the ship starts to reappear.

What makes this detective so special is how it looks at the scene. Instead of just looking at one ship, it draws a Spatio-Temporal Graph. Imagine a spiderweb where every ship is a node (a dot) and the lines connecting them represent how much they influence each other. If two ships are close, the web is tight; if they are far, the web is loose. This web changes shape every second as the ships move. The system uses this living, breathing web to understand that if Ship A turns, Ship B might have to turn too.

Furthermore, this system is brilliant at handling the "what if" factor. In the real world, a ship might have three safe options: turn left, turn right, or go straight. Old computers often got confused and picked a "middle" path that wasn't actually safe or realistic. But because STGDPM starts with total chaos (the blurry mess) and slowly cleans it up, it naturally produces multiple different clear paths. It can show you one scenario where the ship turns left, another where it turns right, and a third where it goes straight, just like a crystal ball showing different possible futures.

The researchers tested their idea using real data from the Caofeidian Waters and Tianjin Port in China. They fed the computer 293,636 ship paths from Caofeidian and 191,106 from Tianjin. The results were impressive. When they compared their new method against older, well-known models (like LSTM, Social-GAN, and Social-STGCNN), STGDPM was the clear winner. For example, when predicting where a ship would be 15 steps into the future in the Tianjin Port, the old models made errors of around 0.2 to 0.4 units (where the unit is a specific measurement of distance), but STGDPM only made an error of 0.142. In the Caofeidian waters, it was even better, with an error of just 0.130.

The team also showed that their system could handle tricky situations, like a ship suddenly speeding up or slowing down to let another pass. While other models got confused and drew paths that didn't match reality, STGDPM stayed accurate. They even proved that every part of their system mattered. When they removed the "spiderweb" graph part, the accuracy dropped. When they removed the "noise-removing" network, it got worse. It seems that combining the dynamic map of the ships with the "reverse chaos" trick is the secret sauce.

In short, this paper suggests that by treating ship prediction as a process of cleaning up a noisy, blurry picture while keeping an eye on how ships interact with each other, we can predict the future of maritime traffic much more accurately. It doesn't just guess one path; it understands that the ocean is full of possibilities, and it gives us a better way to see them all, potentially helping to keep our oceans safer and our cargo moving smoothly.

Technical Summary: STGDPM – Vessel Trajectory Prediction with Spatio-Temporal Graph Diffusion Probabilistic Model

1. Problem Definition

Vessel trajectory prediction is essential for maritime traffic safety and collision avoidance. However, predicting future vessel motion faces two primary challenges:

Complex Interactions: Vessel navigation is heavily influenced by surrounding vessels. Traditional aggregation-based methods (e.g., summation or averaging of neighbor features) often fail to capture the varying importance of different neighbors, while standard Transformer-based models struggle with irregular time intervals and dynamic spatial relationships due to fixed positional encodings.
Behavioral Multi-modality: For a single historical trajectory, multiple safe and reasonable future paths may exist. Existing methods often rely on binary Gaussian distributions (limiting multi-modality to the endpoint) or Generative Adversarial Networks (GANs) and Conditional Variational Autoencoders (CVAEs), which may fail to cover discontinuous manifolds of future paths or converge to mean distributions.

The paper addresses the need for a framework that can comprehensively model dynamic spatio-temporal interactions and the inherent uncertainty (multi-modality) of vessel behavior.

2. Methodology

The authors propose STGDPM (Spatio-Temporal Graph Diffusion Probabilistic Model), a framework that integrates Spatio-Temporal Graph (STG) modeling with Denoising Diffusion Probabilistic Models (DDPMs).

2.1 Dynamic Graph Representation

Vessel interactions are modeled as dynamic graphs $G_t = (V_t, E_t)$ at each time step.

Nodes ( $V_t$ ): Represent vessel positions.
Edges ( $E_t$ ): Represent interaction strength, defined by an inverse squared distance function within a specific interaction boundary $\tau$ . This forms a weighted adjacency matrix $A_t$ that evolves over time.

2.2 Conditional Diffusion Framework

The trajectory prediction task is framed as an inverse process of motion uncertainty diffusion:

Forward Process: The ground truth future trajectory $y_0$ is progressively corrupted with Gaussian noise over $K$ steps to become pure noise $y_K$ .
Reverse Process: The model learns to reverse this diffusion, starting from random noise and iteratively denoising it to recover the predicted trajectory $\hat{y}$ , conditioned on historical trajectories $x$ and the dynamic adjacency matrix $A$ .
Objective: The model minimizes the Mean Square Error (MSE) between the predicted noise and the actual noise added during the forward process.

2.3 Traj-UGnet Architecture

To handle the dynamic graph inputs within the diffusion model, the authors propose a novel denoising network called Traj-UGnet:

Structure: A U-shaped network combining historical trajectories ( $x$ ) and noisy future trajectories ( $y_K$ ) along the time axis.
Core Component: The network utilizes Residual Blocks containing a DynamicGraphConv module.
DynamicGraphConv: This module performs spatio-temporal aggregation using the dynamic adjacency matrix $A$ . It normalizes the graph structure and applies learnable convolutional weights to fuse features across vessels and time steps, allowing the model to adapt to changing interaction topologies.
Process: The network follows a down-sampling and up-sampling path, concatenating skip connections to preserve spatial and temporal details, ultimately outputting the denoised trajectory.

3. Key Contributions

The paper outlines three primary contributions:

First Integration of STG and Diffusion: To the authors' knowledge, this is the first work to integrate Spatio-Temporal Graph models with diffusion models specifically for vessel trajectory prediction, aiming to capture complex spatio-temporal dependencies and inherent uncertainties.
Traj-UGnet Design: The proposal of a specific denoising network (Traj-UGnet) within the diffusion framework, designed to effectively extract spatio-temporal features from dynamic vessel interaction graphs.
Empirical Validation: Extensive experiments on real-world Automatic Identification System (AIS) data demonstrating the model's superiority over existing baselines and its ability to model trajectory behavioral multi-modality.

4. Experimental Results

The model was evaluated on two real-world datasets: Caofeidian Waters (CFW) and Tianjin Port (TJP).

4.1 Quantitative Performance

Using Average Displacement Error (ADE) and Final Displacement Error (FDE) as metrics, STGDPM outperformed state-of-the-art baselines including LSTM, Seq2Seq, Social-STGCNN, Social-GAN, and MID (a diffusion-based Transformer model).

Tianjin Port (15 steps): STGDPM achieved an ADE of 0.142 and FDE of 0.240, significantly lower than Social-STGCNN (ADE: 0.224) and Social-GAN (ADE: 0.214).
Caofeidian Waters (15 steps): STGDPM achieved an ADE of 0.130 and FDE of 0.205, outperforming all other methods.
Ablation Studies: Removing key components (U-Net structure, DynamicGraphConv, or Residual connections) resulted in substantial performance degradation. Specifically, the addition of the U-Net structure improved ADE by approximately 64.1% (from 0.315 to 0.113). The inclusion of DynamicGraphConv further improved ADE by approximately 5.3% (from 0.113 to 0.107). The full model (including Residual connections) achieved a final ADE of 0.094, representing a 70.1% improvement over the baseline model without the U-Net structure (0.315).

4.2 Qualitative Analysis

Accuracy: Visual comparisons showed that STGDPM predictions closely followed ground truth trajectories in complex scenarios (turning, acceleration) where other models deviated significantly.
Multi-modality: The model successfully generated diverse, plausible future paths, including behaviors compliant with the International Regulations for Preventing Collisions at Sea (COLREGs), such as "starboard rule" yielding and course adjustments.

5. Significance and Claims

The paper claims that STGDPM represents a significant advancement in maritime trajectory prediction by:

Addressing Multi-modality: Unlike methods that converge to a single mean path or struggle with discontinuous distributions, the diffusion approach explicitly simulates the evolution of uncertainty, allowing for the generation of multiple plausible future trajectories.
Dynamic Interaction Modeling: By treating interactions as dynamic graphs rather than static aggregations, the model better captures the nuanced, time-varying dependencies between vessels.
Practical Application: The authors state the method holds potential for maritime applications such as autonomous navigation, intelligent collision avoidance, and abnormal behavior detection, thereby enhancing the safety and efficiency of maritime traffic management.

The authors conclude that while the current results are promising, future work will focus on improving model scalability, interpretability, and integrating these diffusion-based STGNNs with emerging technologies for broader real-world deployment.