Generative Human Trajectory Recovery via Embedding-Space Conditional Diffusion

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Claim&Evidence, Rela To Literature:

We introduce critical innovations that distinguish it from existing works:

a)Handling Discrete Locations via Embedding-Space Diffusion. Existing diffusion models for trajectories (e.g., DiffTraj) focus on generating continuous GPS coordinates or simulating synthetic mobility. In contrast, human trajectory recovery involves sparse discrete locations (e.g., check ins), which cannot be directly modeled by continuous-value diffusion (sparse GPS numerical points are not enough for such training).

As mentioned in the Sec 4.1 line 190, one-hot embedding is just one of the methods that can be applied (it is welcome to change by user and not our main research focus). We transform discrete locations into embeddings and performing denoising in this latent space,preserving spatial relationships and decode embeddings back to discrete IDs using an explicit matching process (Sec 4.3) through a stable end to end training (This will be very difficult if people know diffusion well, this model is not only catering for diffusion MSE loss).

b)Conditional Diffusion with Spatial-Temporal Guidance: DiffMove explicitly incorporates historical trajectories and spatial-temporal dependencies through 3 novel modules: 1)Spatial Conditional Block combines our new TGGNN (for transition patterns) and cross-attention (for periodicity) to model complex mobility dynamics. 2)Target Conditional Block fuses temporal length and historical trajectory embeddings to guide imputation targets and 3) Denoising Network Block.

c)To our knowledge, no existing study has designed diffusion models that integrate the diffusion step t embedding with the learning of Graph-based spatial transitions, as detailed in Sec 4.2 TGGNN (also add a figure here in the link https://anonymous.4open.science/r/A01D/README.md).

Method & Eval Criteria:

Foursquare and Geolife datasets with variations (Table 6) serve as standard benchmarks in trajectory recovery research. DiffMove’s design inherently supports adaptability to diverse mobility data:

1. Handling Diverse Mobility Patterns: Foursquare (urban check-ins) and Geolife (normal trajectories) already represent fundamentally different scenarios (sparse POIs vs. normal GPS).

2. Generalization Ability to Varied Missing Ratios:In Table 6, Distance metric performance of DiffMove with 80% missing ratio even outperforms TRILL with 40% missing rate. This demonstrates resilience to extreme sparsity, a key challenge across datasets.

3. Flexible Preprocessing: As noted in Appendix A.8, DiffMove partitions regions into arbitrary geo region sizes (e.g., 0.25 km²) and adapts to variable time intervals. This flexibility ensures applicability to datasets with varied spatial/temporal granularity.

Exp Design Or Analyses:

Such comparisons would be inappropriate for our problem setting:

Fundamental Task Mismatch: Continuous trajectory diffusion models (e.g., DiffTraj) generate GPS coordinates or simulate synthetic mobility. In contrast, human trajectory recovery deals with discrete locations (e.g., sparse IDs), requiring modeling of transitions between categorical IDs and periodicity. It cannot be directly modeled by continuous-value diffusion (sparse GPS numerical points are not enough for such training).

Our baselines (AttnMove,PeriodicMove,TRILL) are widely recognized and remain the standard benchmarks for this problem setting. Regarding more recent baseline, we discussed TERI (Chen et al., VLDB 2024) cited in our related work. We have been working hard on setting up a common problem setting,where our model still outperforms SOTA baseline as shown below in this problem setting.

Essential References:

There are task mismatches, they are primarily designed for trajectory prediction in an image (more specifically is a computer vision trajectory problem), aiming to generate future movement trajectories in continuous space (x,y in the image, using dense CV dataset of ETH and UCY). In contrast, our work specifically addresses trajectory recovery for human mobility in locations (a real-world geographical problem, not the trajectory in image), where trajectories are represented as discrete location IDs requiring historical periodicity and spatial transition modeling.

Q1:

Our method accounts for variations in trajectory length through a standardized data preprocessing pipeline (Appendix A.8). Specifically, we discretize each day into a fixed number N of time slots, where the time interval is a configurable parameter. Trajectories with shorter length than N are padded, ensuring that every trajectory is represented uniformly. This approach enables our model to handle variable-length trajectories effectively.

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Claims&Evidence:

We clarify how existing experiments explicitly demonstrate DiffMove’s superiority in complex, irregular, and uncertain scenarios:

1. Probabilistic Generation vs. Deterministic: Table 1 and 3 shows that sampling multiple trajectories (DiffMove) improves Recall@1 by 1.7–1.85% over single-sample generation. This directly validates our claim that probabilistic diffusion captures uncertainty in human mobility, whereas deterministic baselines cannot.
2. Robustness to Extreme Sparse and Irregularity: Table 6 (Appendix A.10) tests DiffMove under different missing ratios. For example, Distance metric performance of our DiffMove with 80% missing ratio even outperforms TRILL with 40% missing rate and surpasses both PeriodicMove and Attnmove, even when they have lower missing rates 20%.
3. Due to the page limit, including other unnecessary case study (more on cherry picking certain special cases), while small valuable, would extend the scope and length of the manuscript beyond the intended focus. DiffMove demonstrates significant improvements across different missing ratios (Table6). These experiments simulate sparse, irregular, and uncertain scenarios (e.g., through random masking), and our method consistently outperforms baselines in recall and distance metrics. This already provides empirical evidence of the effectiveness of our approach. We will clarify these in the revised manuscript.

Rela To Literature:

DiffMove’s technical design and problem focus are distinct from the cited works, as detailed below:

Unlike CSDI which handles continuous numerical sensor time series (e.g., temperature), DiffMove tackles the fundamentally different challenge of recovering discrete location IDs and is designed as an entirely new framework of embedding-based diffusion and decoding to categorical space (Sec. 4.3) by a single end to end training. It is rather than raw continuous numerical space (unlike CSDI’s simple and single regression-style output).

Another difference is Trajectory-Specific Architecture: Our model introduces spatial-temporal conditioning (new TGGNNs + cross-attention) features and decoding features for human mobility patterns (Sec. 4.2), which CSDI lacks.

Moreover, unlike RNTrajRec and Diff-RNTraj—which rely on vehicles and road network constraints (next road has to be adjacent to the current road) —our approach is designed for scenarios where such road external priors are unavailable, which is fundamentally different problem setting and technical design. RNTrajRec use a transformer to infer missing points deterministically, leveraging road network constraints (e.g., road segments) to guide the predictions. Diff-RNTraj combines diffusion modeling with road network constraints, processes continuous GPS and road graphs and focuses on synthetic generation, not recovery of real-world human sparse trajectories. In contrast, our innovative Spatial Conditional Block and Target Conditional Block (Sec 4.2) are differently engineered to capture the human trajectories’ complex interplay between spatial and temporal dependencies.

Other Suggestions:

Thank you for your valuable feedback.

1. We add a schematic diagram in below link for TGGNN module would enhance intuitive understanding in the revised manuscript. https://anonymous.4open.science/r/A01D/README.md

2. Our method is trained using a masked recovery framework, where we mask certain locations in the trajectory and train the model to recover them based on the observed data, with ground truth available for validation. Once the model is fully trained, we simply apply the same recovery mechanism to infer the real missing locations. DiffMove’s inference process for missing locations is explicitly detailed in Section 4.3 and Appendix A.4. During inference:

Step 1: The model uses observed locations in the current trajectory and historical data to condition the diffusion process. Step 2: Noisy embeddings for missing slots are iteratively denoised via the reverse diffusion process (Eq. 4–5), guided by Spatial/Target Conditional Blocks. Step 3: Decode denoised embeddings.

Questions:

DiffMove leverages contextual information from adjacent time slots and the overall spatial-temporal patterns learned during training to infer the most plausible value for that slot. 1. Transition Patterns: The Sec. 4.2.1 models transitions between locations, inferring k from neighboring observations. 2. Periodicity: Cross-attention identifies recurring patterns (e.g., daily routines) across historical days, even if k-th slots are missing. 3.Global Mobility Knowledge: The embedding table E encodes universal location semantics (e.g., "office" vs. "home"), enabling recovery via similarity matching. 4.Empirically it is validated by our robustness study (Table 6). It shows DiffMove with 80% missing data outperforms all baselines. This demonstrates robustness to extreme sparsity, including scenarios where critical slots are missing.

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W2:

They are shown as the first two equations in eq 6. Actually this is to treat trajectory embeddings as sessions and $e_0^{ob}$ and $e^{hist}$ are integrated using session based graph methods (Xu et al., 2019) and explained in Appendix A.1. We will revise section 4.2 and add a schematic diagram in below link for the TGGNN (yes, a new method proposed) module would enhance intuitive understanding. https://anonymous.4open.science/r/A01D/README.md

W1&W3:

Our work focuses on free-space trajectory recovery where data can be from either case of discrete normal location grid IDs and sparse irregular check ins and data points are not constrained by roads, a special setting that differs from the listed papers.

TAU is a different problem (next POI) from our work which focuses directly on trajectory recovery. TrajBERT and TrajWeaver either operate under different assumptions (e.g., leveraging road network constraints, normal grid IDs only or continuous GPS) or target slightly different objectives,e.g., next POI or trajectory generation (creating new trajectories from scratch). TrajWeaver works directly with continuous GPS coordinates, and the datasets used are smooth taxi trajectories (points laid on road networks) collected in Xi’an and Cheng Du. These differences highlight a key distinction in problem settings. Our baselines’ problems proposed by AttnMove, PeriodicMove, and TRILL, have been widely used in the literature for this specific problem setting, ensuring fair comparisons.

Given the most listed models are not providing their source code yet, regarding new recent baselines, we discussed TERI (Chen et al., VLDB 2024) cited in our related work. We have been working hard on setting up a common problem setting, manage to settle the necessary data pipeline to fit the TERI and get this model run, where our model still outperforms SOTA baselines as shown below in this problem setting.

W4:

While we agree that visualizations can provide intuitive insights, the denoising process in our method occurs at the embedding level rather than in the direct data space (e.g., raw trajectory points or maps). Visualizing these high-dimensional embeddings would offer very limited interpretability. Instead, the effectiveness is shown quantitatively through our results as shown in Table1,2,6,Fig3-9.

Theoretical Claims:

Eq5 can be surely derived based on eq3 (refer to page4 of cited CSDI) due to space limit, we will add to revised manuscript.

Q2 &Q4:

It refers to the limitations of deterministic trajectory recovery methods in capturing the full complexity of spatial-temporal dependencies in low-sampling scenarios. Next location recom do not address the challenges of reconstructing entire trajectories with many missing points. Our choice to use a diffusion model is driven by iteratively refining noisy inputs, naturally generate a distribution of plausible trajectories rather than a single deterministic outcome. Other generative models such as VAE or GAN usually suffer from issues like mode collapse, unstable training dynamics, and difficulty in accurately modeling complex spatial-temporal dependencies; Our diffusion-based approach leverages a probabilistic framework that not only captures the inherent uncertainty in the data but also better models the interplay between spatial relationships and temporal patterns. We include an intro schematic here with the link in W2.

Q3:

Time slot 2 would be treated as missing. It is important to emphasize that our framework is not inherently tied to the 30-minute/1 hour interval and can easily adapt to other interval lengths, such as 10 minutes or even finer resolutions like a parameter for preprocessing. Regarding multiple check-ins within the same time slot, we aggregate these such as the most frequent check-in (adopted in prior works). Repeated check-ins across consecutive slots would be considered observed for each slot. The distance factors are considered in the evaluation metrics. This setting is proposed by prior baselines such as AttnMove. Spatial relationships are instead modeled by our Spatial Conditional Block.

Q5:

The two losses serve complementary purposes, a good balance between predictive accuracy and model generalization. Experimentally, these losses are initially printed during training and there seems to be not big differences in scale. Since we also haven’t treated this weight choices as a more advanced optimization problem (which is not our main focus) and we follow this also inspired by Gong et al. (2022) referenced in line 302, which demonstrated the utility of similar balanced weighting in diffusion models applied in NLP.

Thanks for your valuable comments and stating our evaluations on multiple datasets are good, claims are clear and convincing. Our responses to other parts are as below:

W(i):

Recovering sparse human trajectories, particularly those involving Points of Interest (POIs), significantly enhances various mobility-related applications. By accurately reconstructing incomplete trajectory data, we can improve POI recommendations, leading to more personalized and relevant suggestions for users. Additionally, comprehensive trajectory data supports better urban planning and traffic management by providing insights into movement patterns and congestion areas. Location-based services, such as targeted advertising and ride-sharing, also benefit from complete trajectory information, resulting in improved user engagement and operational efficiency. Overall, the ability to recover and utilize complete trajectory data is crucial for advancing various applications that rely on understanding human mobility. We will clarify this in the revised manuscript to make readers easier to understand.

W(ii):

The term "ID-based representations" refers to how locations are discretized into identifiable points (e.g., POI locations or geographical grid cells) rather than being represented as continuous GPS coordinates. As mentioned in Section A.8 Data Preprocessing, we used publicly available online map services to define the geographical partitioning of the study areas (Tokyo and Beijing) into 500m x 500m blocks. This partitioning provides a grid-based ID representation of locations. This is commonly used in mobility data analysis where raw GPS trajectories are mapped to meaningful locations, making it easier to handle data sparsity and improve interpretability. The baselines—AttnMove proposed this, and PeriodicMove, TRILL focus on the same data preprocessing, which aligns with our problem setting. We will clarify this in the revised manuscript.

W(iii):

Yes, recall is a relevant metric for trajectory recovery, especially when evaluating how well the model retrieves missing locations. Given that real-world applications prioritize capturing as many true missing locations as possible, recall helps assess the effectiveness of the model in recovering essential trajectory points. The baselines—AttnMove, PeriodicMove, and TRILL focus on the same trajectory recovery task, which aligns with our problem setting and they also proposed the same evaluation metrics earlier, so we continue to do the fair comparison with them on this. Other works in trajectory imputation and POI recommendations also utilize recall as a key performance indicator, aligning with our evaluation approach.

W(iv):

Ok, noted on the minor change. We will modify "%Improv. " to "%Improvement" in the table of the revised manuscript.

Supplementary Material:

We think your answer no is by mistake or misunderstanding maybe. Just for information only, we have supplementary materials which include implementation details and code. We include additional details on data processing, model design, and other experiments such as efficiency and scalability study in the supplementary material and appendices.

Overall, thanks for your positive and insightful feedback.