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Coarse-to-Fine Multi-Resolution Diffusion Models for Trajectory Generation in Urban Systems

Wen Ye, Muyan Weng, Chuizheng Meng, Hao Niu, Yizhou Zhang, Yan Liu

arXiv:2608.14570v1cs.LG

TL;DR

Large-scale public trajectory data is limited by privacy constraints, while existing synthetic methods often overlook mobility patterns across spatial and temporal resolutions. MR-Traj uses coarse-to-fine diffusion over milestone trajectories and local segments, achieving comparable global similarity, improved fine-resolution fidelity, and strong downstream utility.

  • Problem

    Large-scale mobility data is restricted by privacy constraints, while existing synthetic trajectory methods often overlook patterns across spatial and temporal resolutions.

  • Method

    MR-Traj uses coarse-to-fine diffusion to jointly model coarse milestone trajectories and fine-grained segments for synthetic trajectory generation.

  • Results

    MR-Traj matches state-of-the-art global distribution similarity while improving fine-resolution fidelity and supporting downstream mobility tasks.

  • Takeaways & Limitations

    MR-Traj supports realistic and useful synthetic mobility data generation while improving resistance to trajectory linkage attacks.

  • Takeaways & Limitations

    Training on taxi datasets from specific urban regions may limit generalizability to other cities or mobility contexts.

Abstract

from arXiv · show

Understanding human mobility is critical for a wide range of urban applications, including traffic management, epidemic control, and urban planning. However, due to privacy concerns, the availability of large-scale public trajectory data remains limited, posing challenges for downstream mobility analysis. Existing methods for synthetic trajectory generation primarily focus on matching global distribution similarity, while often overlooking mobility patterns across different spatial and temporal resolutions that are essential for practical utility. To address these challenges, we propose a novel multi-resolution diffusion framework, MR-Traj, for large-scale trajectory generation. MR-Traj explicitly models trajectories as compositions of coarse-grained milestones and fine-grained segments, enabling the capture of complex spatial-temporal dependencies at multiple resolutions. Experimental results demonstrate that MR-Traj achieves comparable performance to state-of-the-art methods in terms of global distribution similarity, while consistently outperforming them in modeling fine-resolution mobility patterns and supporting downstream urban mobility tasks. In addition, by introducing stochasticity at multiple resolution levels, MR-Traj generates more diverse trajectories, which empirically reduces trajectory linkage risk under a seed-guided data release setting. Our code is available at https://github.com/Ray0202/MR-Traj.

1 Introduction

Large-scale mobility data is valuable for urban applications but constrained by privacy and regulatory concerns, while existing synthetic trajectory methods often underrepresent fine-resolution patterns and downstream utility. MR-Traj addresses these limitations with a two-level diffusion framework that generates coarse milestones and conditioned fine-grained segments, achieving comparable global similarity, improved local fidelity, downstream utility, and lower empirical linkage risk.

  • Motivation: Mobility data supports urban planning, traffic estimation, epidemic control, and location-based services, but large-scale access is restricted by privacy and regulatory constraints.These constraints motivate synthetic trajectory generation for urban mobility analysis.
  • Limitations: Existing methods predominantly minimize global distribution discrepancies, despite mobility tasks often operating on partial trajectories or localized segments that require fine-resolution fidelity.Urban mobility includes both long-range global structure and fine-grained local behavior across spatial and temporal resolutions.
  • Method: MR-Traj uses milestone-level diffusion to capture global trajectory structure and segment-level diffusion to generate fine-grained movements conditioned on synthesized milestones.The framework jointly models global milestone trajectories and local trajectory segments under metadata guidance.
  • Results: MR-Traj achieves performance comparable to state-of-the-art methods in global distribution similarity while consistently improving local distribution fidelity.This evaluation is reported on large-scale real-world mobility datasets.
  • Downstream Utility and Privacy: MR-Traj supports taxi destination prediction and anomalous mobility pattern identification while exhibiting lower empirical linkage risk than existing metadata-guided baselines.The framework introduces stochasticity through its multi-resolution generation design, supporting responsible synthetic data release.

2 Related Work

Prior trajectory-generation work spans Markov models, deep generative models, and diffusion methods, with growing emphasis on hierarchical resolution and downstream utility. MR-Traj builds on these advances by separately modeling global structure and local segments in a multi-resolution diffusion framework.

  • Markov-based methods: Markov-based methods model trajectories autoregressively, using previous locations and, in extensions, contextual information in latent processes.These approaches are interpretable but their autoregressive sampling limits scalability and prevents efficient parallel generation.
  • Deep generative models: VAEs and GANs became widely used for trajectory synthesis, with recurrent architectures such as LSTMs modeling temporal dependencies.TrajGANs was an early representative GAN-based trajectory-generation method.
  • Deep generative models: Hierarchical VAEs provide probabilistic trajectory-generation frameworks, but can produce overly smooth trajectories and miss complex fine-grained mobility patterns.VOLUNTEER uses a two-layer VAE that infers user-level latent attributes before generating conditioned trajectories.
  • Diffusion models: Diffusion models offer stable training and flexible conditioning, and have shown strong performance for complex spatio-temporal trajectory data.DiffTraj demonstrates that diffusion probabilistic models can generate synthetic trajectories closely matching real mobility distributions under metadata conditioning.
  • Hierarchical and multi-resolution modeling: Coarse-to-fine and multi-resolution approaches separate global planning from local refinement, while recent work emphasizes controllability and downstream urban analysis beyond distributional similarity.MR-Traj extends this direction by modeling global trajectory structure and local segments separately to capture multi-scale dependencies and improve analytical utility.

3 Preliminaries

This section defines trajectories at continuous and discretized spatial scales and frames synthetic generation as preserving spatial-temporal mobility patterns for downstream analysis. It motivates multi-resolution modeling because global distribution similarity alone may not ensure utility, while multi-level noise can increase trajectory diversity.

  • Trajectory Representation: A trajectory is a regularly sampled sequence S = [s_1, ..., s_n] whose points use latitude-longitude coordinates or grid IDs, with n denoting its length.The dual representation supports precise spatial processing and discretized spatial processing.
  • Synthetic Trajectory Generation: Synthetic trajectory generation seeks trajectories S′ that preserve the spatial-temporal characteristics and patterns of real trajectories for downstream tasks such as traffic management and mobility behavior analysis.The generated data should mimic real-world mobility patterns and support spatial-temporal analysis.
  • Utility Motivation: The theoretical motivation states that reducing global total variation distance between real and synthetic distributions is essential but insufficient for maximizing downstream utility.Utility also depends on local trajectory patterns when the observed fraction may be any segment of a complete trajectory.
  • Multi-Resolution Motivation: Multi-resolution modeling is motivated as a way to capture local trajectory patterns and increase synthetic-trajectory diversity through noise injected at multiple resolution levels.Noise at various stages creates a broader range of possible synthetic outcomes, supporting the privacy rationale for the design.

4 Methodology

MR-Traj uses a coarse-to-fine framework with separate milestone-level and segment-level diffusion models. Milestones provide global structure, while conditioned segment generation reconstructs coherent fine-resolution trajectories.

  • Multi-resolution framework: MR-Traj decomposes trajectory generation into milestone-level and segment-level diffusion models spanning Origin-Destination, milestone, and complete-trajectory resolutions.The framework treats Origin-Destination pairs as the most abstract resolution, milestones as intermediate structure, and segments as the finest resolution.
  • Milestone extraction: Milestones abstract complete trajectories across spatial and temporal resolutions, with uniform sampling and open angle extraction considered as derivation strategies.Uniform sampling selects one point every α points and is designed for dense GPS trajectories without semantic or POI annotations.
  • Milestone extraction: Uniform sampling preserves trajectory shape, standardizes milestone intervals, and creates equal-length segments that simplify segment-level diffusion modeling.The paper reports uniform sampling as more effective for its setting in the Section 5 ablation study.
  • Segment-level diffusion: Segment generation is conditioned on segment attributes and corresponding start and end milestones, ensuring local realism and coherence within the complete trajectory.Each generated segment starts and ends at milestone points, which provide guidance for connecting segments.
  • Inference: During inference, synthetic milestones generated by the milestone-level model replace training milestones to guide segment generation, with variable-length trajectories handled by interpolation-based resampling.The same attribute information is used during training and inference.

5 Experiment

MR-Traj is evaluated on Chengdu and Porto taxi trajectories for distribution similarity, downstream utility, and privacy. It matches strong global baselines, improves regional and downstream mobility fidelity, and enhances privacy through multi-level stochasticity.

  • Experimental Setup: Experiments use Chengdu and Porto taxi trajectory datasets to evaluate distribution similarity, downstream utility, and privacy under seed-guided release.Trajectories shorter than 10 points were filtered, and Porto analysis focused on its central kernel region.
  • Distribution Similarity: MR-Traj achieves close parity with DiffTraj on global distribution metrics while outperforming all baselines on regional segment similarity across both datasets.Evaluation uses a 16 × 16 spatial grid, with cells covering less than 1 km^2; generated trajectories retain precise GPS locations.
  • Downstream Utility: 2.361 Haversine Distance Error for MR-Traj trained on synthetic data closely approaches the 2.319 error for the original-data model in taxi destination prediction.The task predicts a taxi trip’s destination from a partial trajectory using T-CONV.
  • Downstream Utility: MR-Traj achieves the highest cosine similarity for anomalous mobility patterns at both global-hourly and weekly-hourly scales.Chengdu lacks weekly-hourly evaluation because its dataset has no departure-date information for grouping trajectories by week.
  • Privacy: MR-Traj obtains lower privacy-linkage scores than DiffTraj across all metrics by injecting noise at both structural and fine-grained trajectory levels.Independent segment sampling guided by generated milestones makes the original metadata harder for adversaries to reverse engineer without compromising realistic utility.

6 Ablation study

The ablation study evaluates MR-Traj design choices and uniform milestone sampling rates on the Porto and Chengdu datasets. All tested variants underperform the original MR-Traj in distribution similarity and downstream utility, while sampling-rate analysis examines abstraction effects.

  • Configuration ablations: Table 4 evaluates four MR-Traj configurations on the Porto Dataset, including alternative milestone extraction, location guidance, and segment-generation designs.The alternatives replace uniform milestone sampling, use precise rather than discretized start and end locations, or condition segment generation on multiple milestones.
  • Configuration ablations: All MR-Traj variants perform worse than MR-Traj in both distribution similarity and downstream utility, validating the original design choices.The comparison supports using the original configuration rather than the ablated milestone, guidance, or segment-generation variants.
  • Sampling-rate analysis: The study analyzes uniform sampling rates 15, 35, and 55 on the Chengdu dataset for their effects on distribution similarity and downstream utility.Sampling rate 5 is excluded because Chengdu trajectories are densely sampled, so extracting milestones every five timestamps provides virtually no abstraction.

7 Conclusion

MR-Traj is a multi-resolution diffusion framework that combines milestone-level global structure with segment-level local refinement to generate realistic synthetic mobility trajectories. Experiments show comparable global similarity, improved fine-resolution fidelity and downstream utility, and lower linkage success through multi-level stochasticity.

  • 7 Conclusion: MR-Traj models milestone-level global structure and segment-level local refinement to capture multi-scale spatial-temporal dependencies while preserving fine-grained trajectory details.This supports realistic long-range movement patterns and detailed synthetic trajectories.
  • 7 Conclusion: MR-Traj achieves performance comparable to state-of-the-art diffusion baselines in global distribution similarity while consistently improving fidelity at finer spatial resolutions.The results emphasize the importance of explicitly modeling local trajectory segments for high-quality synthetic data generation.
  • 7 Conclusion: Generated trajectories demonstrate strong downstream utility for taxi destination prediction and anomalous mobility pattern identification, retaining informative mobility behaviors.These results extend evaluation beyond distributional metrics.
  • 7 Conclusion: Under a seed-guided release setting, multi-level stochasticity reduces linkage success compared to single-level diffusion approaches without sacrificing utility.This indicates improved resistance to linkage attacks while maintaining practical usefulness.
  • 7 Conclusion: Overall, MR-Traj balances realism, utility, and privacy in synthetic spatiotemporal data through multi-resolution generative modeling.The framework provides realistic and useful synthetic mobility data with improved resistance to linkage attacks.

8 Limitations and Ethical Considerations

MR-Traj retains privacy, geographic, behavioral, and metadata-related limitations despite strong empirical performance. Synthetic trajectories should therefore be released with safeguards and used responsibly, especially outside safety-critical decision-making.

  • Privacy: Multi-level noise injection reduces trajectory linkage risk, but stronger adversarial settings may still expose residual privacy information.Appropriate safeguards should accompany any synthetic trajectory release.
  • Generalizability and Bias: Training on taxi datasets from specific urban regions may introduce geographic and behavioral biases and limit generalizability to other cities or mobility contexts.Metadata-conditioned generation may also propagate biases present in the original data.
  • Responsible Use: Synthetic trajectories should support downstream analysis but not replace real-world data in safety-critical applications such as policy-making or infrastructure planning.The authors encourage responsible use and continued research on privacy protection and robustness.

9 GenAI Disclosure

Generative AI tools were used only to polish language and improve presentation clarity, not to develop, process, analyze, design, or derive conclusions for the study.

  • AI use disclosure: Generative AI was used solely for language polishing and presentation clarity, with authors retaining full responsibility for the paper’s content.The tools were not involved in methodology development, data processing, experimental design, result analysis, or deriving scientific conclusions.

A Dataset Information … D Hyperparameter Setting

The study uses processed Chengdu and Porto taxi trajectories, evaluates synthetic mobility with distributional and pattern metrics, and assesses downstream destination prediction and anomaly identification. Training and inference configurations are summarized alongside the stated GPU setups.

  • A Dataset Information: The study uses Chengdu and Porto taxi trajectory datasets, with Porto containing over one million trajectories sampled every 15 seconds.The Porto data were collected over one year as part of the ECML/PKDD 2015 taxi destination challenge.
  • A Dataset Information: Porto trajectories with fewer than 10 points were removed, and analysis focused on the city’s central kernel region.The kernel region has higher and more uniform trajectory density, whereas Chengdu required no additional spatial filtering.
  • B Evaluation Metrics: Density Error measures spatial-distribution discrepancy between synthetic and real trajectories using Jensen–Shannon divergence.The distributions are evaluated over a discretized spatial grid.
  • B Evaluation Metrics: Distance Error compares total travel-distance distributions between synthetic and real trajectories using Jensen–Shannon divergence.A trajectory’s total distance is the sum of distances between consecutive GPS points.
  • B Evaluation Metrics: Pattern Score measures similarity between frequent discretized-grid movement sequences from synthetic and real trajectories using F1 score.Pattern F1 combines Precision and Recall for real and synthetic pattern sets.
  • C Details of Downstream Tasks: Taxi Destination Prediction uses locally enhanced T-CONV to extract multi-scale spatial patterns and predict destinations from clustered arrival hotspots.Prediction error is measured with Haversine distance between ground-truth and predicted destinations.
  • C Details of Downstream Tasks: Anomalous Mobility Pattern Identification constructs normalized time-dependent mobility vectors, clusters them with mean-shift, and labels sufficiently small clusters as anomalous.The procedure uses cluster-size statistics to determine the anomaly threshold.
  • D Hyperparameter Setting: Hyperparameter configurations for training and inference are summarized in Table 7, with diffusion models using an 80GB A100 GPU and downstream models a 10GB RTX 2080 GPU.The stated hardware assignments distinguish diffusion-model training from downstream-task model training.

E Theoretic Analysis · F Details on Diffusion Model Preliminaries

The theoretic analysis links downstream-task utility to discrepancies between real and synthetic trajectory distributions, motivating joint minimization of conditional and observable-marginal mismatch. The diffusion preliminaries describe DDPMs’ forward noising and learned reverse denoising processes for synthetic trajectory generation.

  • E Theoretic Analysis: Downstream predictors infer trip properties from an observable trajectory fraction, including destination, mileage, and anomalous mobility patterns.These tasks are denoted as g(S_u,S_o), where S_o is the observed fraction of a full trajectory.
  • E Theoretic Analysis: Synthetic complete trajectories train a predictor whose utility is evaluated by square empirical risk on a trajectory distribution.The predictor is trained using trajectories generated by P′(S).
  • E Theoretic Analysis: The optimal synthetic-data predictor is f(S_o) = E_Su∼P′(S_u|S_o)g(S_u,S_o).It takes the conditional expectation under the synthetic distribution given the observable trajectory fraction.
  • E Theoretic Analysis: Under a 1-Lipschitz loss, real-data prediction risk can be bounded using Wasserstein distance and conditional Total Variance Distance.The Wasserstein bound depends on the diameter D of the support set of S_u.
  • E Theoretic Analysis: When the joint real and synthetic distributions are sufficiently close, the analysis bounds downstream risk through their Total Variance Distance and its triangle inequality.The stated closeness condition is Total Variance Distance less than 1.
  • E Theoretic Analysis: The resulting upper bound motivates jointly minimizing ||P(S_u,S_o) − P′(S_u,S_o)||_TV and ||P′(S_o) − P(S_o)||_TV.The first term measures joint-distribution mismatch, while the second measures observable-marginal mismatch.
  • F Details on Diffusion Model Preliminaries: DDPMs generate trajectories by gradually adding noise across timesteps and learning a reverse process that denoises noisy inputs back to realistic samples.Their ability to model complex, high-dimensional distributions motivates their use for synthetic trajectory generation.
  • F Details on Diffusion Model Preliminaries: The learned reverse transition is p_θ(x_t−1|x_t) = N(x_t−1; μ_θ(x_t,t), Σ_θ(x_t,t)), approximating q(x_t−1|x_t).Closed-form sampling of noised inputs provides a more efficient forward process than stepwise noise addition.
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