TrajFlow: Nation-wide Pseudo GPS Trajectory Generation with Flow Matching Models
Authors: Peiran Li
Jiawei Wang
Haoran Zhang
Xiaodan Shi
Noboru Koshizuka
Chihiro Shimizu
Renhe Jiang
Venue: ICLR 2026 Poster (2026)
Keywords: Flow matching
Human Trajectory
Generative modeling
Human mobility
Primary area: generative models
TL;DR: This paper proposed TrajFM, a flow-matching-based GPS trajectory generation model that overcomes multi-scale, diversity, and efficiency limitations of diffusion approaches to enable nationwide, multi-scale, and multi-modal GPS trajectory generation.

Abstract: The importance of mobile phone GPS trajectory data is widely recognized across many fields, yet the use of real data is often hindered by privacy concerns, limited accessibility, and high acquisition costs. As a result, generating pseudo–GPS trajectory data has become an active area of research. Recent diffusion-based approaches have achieved strong fidelity but remain limited in spatial scale (small urban areas), transportation-mode diversity, and efficiency (requiring numerous sampling steps). To address these challenges, we introduce TrajFlow, which to the best of our knowledge is the first flow-matching-based generative model for GPS trajectory generation. TrajFlow leverages the flow-matching paradigm to improve robustness and efficiency across multiple geospatial scales, and incorporates a trajectory harmonization \& reconstruction strategy to jointly address scalability, diversity, and efficiency. Using a nationwide mobile phone GPS dataset with millions of trajectories across Japan, we show that TrajFlow or its variants consistently outperform diffusion-based and deep generative baselines at urban, metropolitan, and nationwide levels. As the first nationwide, multi-scale GPS trajectory generation model, TrajFlow demonstrates strong potential to support inter-region urban planning, traffic management, and disaster response, thereby advancing the resilience and intelligence of future mobility systems.

Published as a conference paper at ICLR 2026
TRAJFLOW: NATIONWIDE PSEUDO GPS TRAJECTORY GENERATION WITH FLOW MATCHING MODELS
Peiran Li
Jiawei Wang2t
Haoran Zhang?
Xiaodan Shi
Noboru Koshizuka
Chihiro Shimizu!
Renhe Jiang?
Hitotsuubshi University "Stockholm University
The University of Tokyo
MoocationMind Inc.
ABSTRACT
The importance of mobile phone GPS trajectory data is widely recognized across many fields, yet the use of real data often hindered by privacy concerns, lim- ited accessibility, and high acquisition costs. As result, generating PSP trajectory data has become an active area of research. Recent diffusion-basee ap- proaches have achieved strong fidelity but remain limited in spatial scale (small urban areas), transportation- mode diversity, and efficiency (requiring numerous sampling steps). To address these challenges, we introduce TrajFlow, which the best of our knowledge is the first flowmmatching-base generative model for GPS trajectory generation. TrajFlow leverages the flow-matching paradigm improve robustness and efficiency across multiple geospatial scales, and incorpo- rates a trajectory harmonization & reconstruction strategy to jointly address seal- ability, diversity, and efficiency. Using a nationwide mobile phone GPS dataset with millions of trajectories across Japan, we show that TrajFlow or its variants consistently outperform diffusion-based and deep generative baselines at urban, metropolitan, and nationwide levels. As the first nationwide, multi-scale GPS trajectory generation model, TrajFlow demonstrates strong potential to support inter-region urban planning, traffic management, and disaster response, thereby advancing the resilience and intelligence of future mobility systems.
INTRODUCTION
Human mobility data particulllllllly the rapidly growing mobile phone GPS data has been widely applied across diverse domains, including urban studies (Chen et al.) 2023 Jin et al. (023), epi- demiological prediction and control (Bao et al. 2020 Zhang et al. 2022). ). and transportation and travel planning (Torre-Basteee Bastida et al. 2018). However, the use of real personal mobility data poses several challenges, such as privacy concerns, limited accessibility, and substantial financial or time costs. Privacy is especially critical, data collection and utilization may reveal sensitive personal details, which in turn makes human mobility datasets difficult to access and share.
Consequently, recent years have witnessed growing number of studies GPS trajectory gener- ation (Zhu et al.) 2023b] Jiang et al.] 2023 Wei et al.) 20224] Zhu et al. 2023a). Notably, several research gaps remain even in sfate-oftthe-- art (SOTA) models for this task: Multi-scale capabil- ity: Existing models primarily focus on urban-level data and struggle to generalize to regional or nationwide scales. This limitation significantly constrains the practical applicability of generated trajectories, as real-world deployment often requires modeling across multiple spatial levels. In particular, maintaining a stable signal-to-noise ratio (SNR) becomes increasingly challenging when extending trajectory generation from block-level movements to citywide or nationwide patterns, un- diversity: Current approaches are largely confined to taxi trajectory data. While taxi GPS traces are valuable,
derscoring the need for models with robust multi-scale capability. Transportation-mn
"Code open-sourced at mulnttps: /ttps://ae /ttptttttbb./t//////////t/.h.hst com/ wtt.///eooottt/aaaeLLL... 1 "Corresponding author. Email: j awei www.i@g.e. @gg ecc. u-tokyo.ac.

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Published as a conference paper at ICLR 2026
Applications limited in scale, variety and efficiency of generation
Large-scale
Urban planning
Disaster Management
Epidemic control
Transportation Plenning and Management
High-Effliienn
Privacy- concern!
MD
Privacy- concern Free
Generate
Real Human Mobility
Pseudo Human Mobility
Nation scale
Urben-scaale
Nation-wide multi-scale multi-mode efficient Pseudo GPS Trajectory Generation
Gap
Goal
Figure I: In pseudo-human mobility generation, three key challenges remain to be addressed: multi- scale capability, transportation-modd diversity, and training & inference efficiency.
real human mobility involves much broader range of transportation modes (e.g.. train, car, bike and walk), which are not adequately represented in existing models. Training/Inferenc efficiency and robustness: Most SOTA methods rely diffusion- based frameworks. Although methods such as DDIM (Denoising Diffusion Implicit Models) can accelerate sampling, they still require iterative denoising and remain computationally expensive. Moreover, recent work has shown that commonly used diffusion objectives are closely related to ELBO-based optimization and can be interpreted as weighted integrals of ELBOs over noise levels (Kingma & Gao (023). By contrast, Flow Match- ing directly regresses the target vector field along a prescribed conditional probability path, and, when instantiated with diffusion paths, has been shown provide a more robust and stable training alternative (Lipman et al. 2022).
To address these limitations, we propose TrajFlow, How-matching-based GPS trajectory genera- tion model designed to produce nationwide, multi-scale pseudo-GiP GaS trajectories. The main contri- butions of this study are summarized as follows:
We present the first flow-mane Now-matching-- based generative framework for GPS tra- jectory modeling, and show that the flow-matching paradigm improves robustness and stability across multi-scale scenarios.
Novel paradigm:
Methodological design:
We integrate trajectory harmonization. OD-conditioned normalization, and bowebased training into a unified framework that jointly addresses scalability, diversity, and efficiency in GPS trajectory generation.
Using a nationwide mobile phone GPS dataset with millions of users, demonstrate that TrajFlow achieves state-of-the-ee performance across urban, metropolitan, and nationwide settings, highlighting its value for large-scale human mobility modeling.
Empirical validation:
RELATED WORK
Human Mobility Generation. Human mobility generation has attracted growing attention across both computer science and social science domains (Feng et al.) 2020) Simini et al.] 2021 Jiaweil al., (0244.. the early stages, before the widespread availability mobile phone positioning data, research primarily relied mechanism-basee approaches. Travel survey data-often
often referred to as travel diaries-were commonly used. Such surveys typically record an individual's daily travel activities, providing detailed information including the sequence of mobility activities and the modes of transportation. These rich datasets enabled the development of activity- based models for human mobility sequence generation (Karamshuk et al. 2001 Hess et al. 2015 Barbosa et al.) 2018). With the growing demand for large-scale mobility data, researchers began to explore alternative sources such as GPS trajectories and call detail records (CDR). For example, TimeGeo (Jiang et al. 2016) ex-
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tended activity- based modeling by leveraging GPS and CDR data. Different from TimeGeo, studies leveraging mobile phone GPS and CDR data have investigated the generation of more realistic ac- tivity patterns by combining deep learning models. For instance, Act2 (Liu et al. 2024) focuses on activity-to-locate
generation, while GeoAvatar (Li et al. [022 2025 achieves individualized trajectory generation, reflecting both temporal regularity and personal heterogeneity. More recently, advances in large language models (LLMs) have allowed for interpretable mobility generation at
relatively higher computation cost (Jawwe al. 2024 Feng al. 2025 Beneduce et al.) 2025).
GPS trajectory generation. As one of the most widely used data sources for representing human mobility, GPS trajectories have become a central focus in generative modeling. A variety of ap-
proaches have been proposed for GPS trajectory generation, ranging from model-based models to
learning-basse frameworks (Yin et al. 2017 Hsu et al. 2024 Zhu et al. 2023b; Wang et al. (021)) Early work often adopted sequence modeling techniques such as Hidden Markov Models (HMMs) and Recurrent Neural Networks (RNNs), including their variants like LSTMs and GRUs (Yu et al, 2019. For example, Song al. (Song al., 2016) applied an HMM-based model predict and simulate large-scale human mobility patterns following natural disasters. Beyond Markovian mod- els, deep generative models such as Variational Autoencoders (VAEs) or generative adversarial net- works (GANs) have been introduced to capture latent mobility representations (Liu et al., 2018 Huang et al. 2019 Chen et al. 202T). More recently, the rapid proliferation of denoising diffu- sion probabilistic models (DDPM) have further advanced GPS trajectory generation. DiffTraj (Zhu
ctt al. 2023b) and its extensions (Wei et al. 2024 Zhu et al. 2024) have shown strong performance
in generating urban-scale taxi trajectories.
PRELIMINARY
3.1 PROBLEM DEFINITION
Definition (Human Mobility (GPS Trajectory)). A human mobility record is represented as tuple (lut, lon, f), indicating that an anonymous user visits a geographic location (specified by latitude and longitude) at time t. A mobility trajectory is then defined records, traj = {lato, long, to), (lati, (t) (lat,, lonn, tx)]. J. In our setting, anonymized data are used, and user identifiers are replaced with random tokens to ensure privacy.
ordered sequence of such
Definition 2 (GPS Trajectory Generation). Given ground-truth dataset of GPS trajectories X (traje, trajer.................. traj." T ), the goal GPS trajectory generation is to synthesize a pseudo-dataset Y {trajy, traje..... ,,raj,,") ). such that Y closely matches the distributional characteristics of X while preserving user privacy.
3.2 FLOW MATCHING MODEL
Flow Matching is powerful class of generative models designed to learn continuous transforma- tions between probability distributions. Unlike diffusion models that rely on a fixed noising process, flow matching models learn vector field vy (x:) that directly models the "flow" of particles from simple base distribution Po (c.g.. a standard Gaussian) to a complex target data distribution p1 (c.g., the distribution of real GPS trajectories).
The core idea is to define a probability path (x) and a corresponding time-dependent vector field (x(x) such that sample Zy ~ Po can be transformed into sample æ1 ~ Pı by solving the ordinary differential equation (ODE) et al. (022). de, di oy (2t), where is the state of a particle at time E [0, 1]. The goal is to train a neural network (o t) to approximate this ground-truth vector field (2r).
A key innovation in flow matching is the objective function. Instead of directly regressing on the often-intractable vector field of the marginal probability path pr. Conditional Flow Matching (CFM) defines a conditional probability path (t (x1) and a corresponding conditional vector field u, 21) that are much simpler to compute. A common choice for the conditional path a simple linear
interpolation between noise sample z6 and data sample .1 pe(x: | (1)) Mix (1 f)ar + tæ d2... However, the simplest and most common formulation, which we adopt, regresses the model directly on the vector field defined by straight path between Zo and 21: uxx xx) 21 -8p-
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The model (1 t) is then trained to predict this vector field us given the point 2t the path. The flow matching objective is a simple regression loss:
LFM = p(x))))) p(zo) v ((1 t)zo + tæ1, t) (x1 xo z0)l
(1)
where & sampled uniformly from [0, 1], 21 is sampled from the real data distribution, and xig is sampled from the prior noise distribution. This objective allows the model learn the complex data distribution stably and efficiently. Once trained, we can generate new data by sampling a point To ~ pu and solving the learned ODE de (z from 0 to using an ODE solver.
TRAJFLOW
4.1 MOTIVATION
Diffusion-baat based models (e.g., DiffTraj) have achieved high-fidelity GPS trajectory generation the urban scale, but when the spatial scale grows, e.g., from urban scale, metropolis scale, and to nationwide scale, observe sharp degradation of accuracy across multiple metrics (see Fig. 2a
Median Fréchet (p10-p90)
Median DTW (p10-p90)
1e
Density
1e4
le5
1.5
Frechet distance
1.0
DTW
0.5
2-
0.0
Central Takyo Tokyya Metropolis Spatial scale
Japan
Central Tokyo
Takyo Metropolls Spatial scale
Japan
Central Tokyyo Tokyo Metropolis
Japan
Spatial scale
(a) The performance of the DiffTraj degrades during multi-scale generation. Each subplot shows one metric across spatial scales (c.g., Central Tokyo + Tokyo Metropolis + Japan).
100
SNR
OUR
ONR 12.33
-3-20
32.5
32
23
25.70
31.00
305
30
SMR d.70
25.0
360
214
1900
30 nat)
543 20 03 50
SMB 19.26
1500 1558 1975 3400
Long fuce
Locghude
Longlade
11.
225
(b) SNR collapses during diffuusion noising procedure. noise parameter suitable for a nationwide scale not suitable for smaller regions (e.g., Tokyo Metropolis).
Figure 2: (a) shows the accuracy degradation of DiffTraj at increasing spatial scales. (b) shows the SNR collapses when applying fixed noising parameter across scales.
We suggest that there are two key reasons why diffusion liffusion-based SOTA models fail to generalize across scales. First, when expanding to larger geographical regions, the subsets of fine- mne-graindd local trajectories become small in magnitude, resulting in an extremely low SNR. In these cases, the weak signal is easily overwhelmed, forcing the reverse process reconstruct fine-grained structures from
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highly noisy inputs. Standard mean squared error (MSE) objectives further intensify this challenge by prioritizing absolute rather than relative eπrоr, thereby aggravating the imbalance across seales. To address this, data harmonization becomes essential: by curating and rescaling data distributions across different spatial scales, we can explicitly compensate for this imbalance and provide a more balanced learning signal (see Sec. (.2).. Second, diffusion models rely on stepwise denoising pro- cess that gradually transforms Gaussian noise into samples, In conditional settings where subsets of data span vastly different numerical ranges-for example, miero-scale local trips versus macro- scale long-dise tingdiittane journeys-the the forward noising process injects noise of nearly fixed magnitude regardless of scale. This scale-invariant noise injection leads fundamental mismatch that duces model robustness. To overcome this limitation, we adopt flow matching as a more suitable alternative: by directly learning the continuous probability flow between simple prior and the tar- get distribution, it sidesteps the fixed-step denoising chain and provides more flexible generative mechanism for multi-scale settings (see Secs. 4.3 and 4.4). In the following, we detail how our proposed framework, TrajFlow, addresses the critical challenges of urban mobility modeling and generates reliable pseudo-GPS trajectories.
GPS Trajectory Harmonization
Trajectory Modeling Architecture
Conditional Input
Z (Z,
Wide Doup enceding
Conditional veclor
Diffusion stop
Transform
Embenningg
Linear map A
Linear map ge
Dencleing reeult
Spanial Space
Festure spare
&
Predicted orign desination
Training Stage
X1
B + Vo
22,
Sy-1 = By (z
T
Generation Stage
With trip condition, reconstruct to real- world Spatial Space
Multi-scale GPS
Trip Conditions
Trajectory
Urban ide
Region-wide
Nationwide
Figure The overview of the proposed TrajFlow.
4.2 MULTI-SCALE GPS TRAJECTORY HARMONIZATION AND RECONSTRUCTION
To address the SNR imbalance across scales, we adopt trajectory harmonization & reconstruction strategy in conjunction with the flow matching framework (see the upper-left panel of Fig. 3 Rather than working directly on raw GPS coordinates, which vary across orders of magnitude, we normalize each trajectory individually, rescaling all points into shared bounded coordinate space. The model thus operates in this normalized space, predicts fine OD location within the given region-level OD zones, together with waypoints under flow matching; afterward, we invert the normalization back to real geographic coordinates. This prevents tiny local displacements from being overwhelmed by large-scale variations, stabilizes gradient magnitudes during optimization, and accelerates conver- gence (loffe & Szegedy 2015).
In addition, enhance the efficiency and stability of model learning, apply a trajectory-feature transformation step that simplifies each trajectory while preserving its essential geometric struc- ture. This kind of segeettor--eatuure transformation reduces the length of the trajectories from to D. where D substantially smaller than L, thereby lowering computational overhead and improving training stability. In practice, the process involves recursively removing points that fall
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within tolerance of the line segment formed by their neighbors, retaining only those points that contribute to the overall geometric shape. As a result, long straight segments are compressed into few representative points, while turning points areas of high curvature are preserved. In this study, we experiment with multiple harmonization methods and find that the classical Ramer- Douglas-Peucker (RDP) algorithm (Ramer 1972) provides the best trade-off between compression and fidelity. Details of this algorithm are presented in the Appendix, A.2
The proposed strategy can be interpreted analogous the mumaliizaioondennrmaaiaaiii pro- cedure in feature preprocessing: trajectories are first compressed into a compact representation to facilitate efficient model training, and subsequently expanded back their original scale for deploy- ment, see Appendix A.2
4.3 GPS TRAJECTORY MODELING ARCHITECTURE
As shown in the upper-right panel of Fig. we adopt the Wide & Deep module (Zhu al. 2023b) to embed the input condition of trajectory, including departure time, OD (zone-level), and trans- portation mode. Concretely, the conditional vector 6, is formed by fusing a linear wide projection of numeric motion/context characteristics with non-linear deep projection of discrete context char- acteristics, and the result e, is injected into every block of the vector field network by (g e,) that parameterizes our probability flow:
dI. = volatttted dt
Inputs and feature partition. The first part of the input is numeric features Zn trajectory-Ievel scalars such as average speed, average inter-point distance, elapsed time, cumulative distance/steps (all standardized). The other part is the discrete features Za including departure time of day, transportation mode, and OD (zone-level).
Wide&Deep encoding. We dimensional vector, denoted as éwide- Each discrete feature in Za is first embedded into an n- dimensional vector; the resulting embeddings are concatenated and passed through two MI.P layers with nonlinearity to produce Edoep. The final condition vector is obtained by fusing the two branches:
linear projection to map the numeric features Zn into n-
ex = LayerNorm (Cwide + Cdeep)
Time embedding. The continuous flow time t E [0, 1] is encoded by a sinusoidal/Fouric mapping followed by small MLP to yield time vector e₁ E Rdd, We combine it with the condition single control signal ē = e + Cz.
Conditional control into the buckbone. Let 19 denote the hidden state of block f. We broadcast to all blocks and inject it an additive, learnable bias
h ( + (1) + A (I=
(4)
where ((8) is the block's transformation and A(9) is learned linear map. This keeps the conditioning pathway lightweight and consistent with the ODE parameterization of the vector field.
4.4 MATCHIGG TRAINING AND INFERENCE
At the training stage (i.e., the middle panel of Fig. B) we use mini-batches of ground-truth tra- jectories that are first harmonized with RDP and then padded to common length using a validity mask. For each trajectory, we compute the numeric and discrete conditions, obtain the condition embedding e, through the Wide& module (Eq. 3. and sample flow time / with noise end- point Z-- The straight-path point 2; and the corresponding target conditional vector field are then constructed according to the flow-matching objective (Eq. []. In addition, we introduce iary supervised loss between the predicted and ground-truth fine OD location to enhance spatial and semantic awareness. Model parameters optimized with masked regression loss over valid to- kens, optionally augmented by smoothness and counded-support regularizers, followed by standard optimizer updates.
auxil-
At the inference stage (i.c., the last panel of Fig. 3) given a trajectory condition (c.g.. departure time, OD (zone-level), transportation mode), we first compute e, using the Wide& encoder and

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prepare the time-embedding schedule. We then initialize zu from the base distribution (e.g.. standard Gaussian noise). The synthetic trajectory is obtained by numerically integrating the learned flow ODE on [0, 1] (Eq. 2). injecting e, at each solver step in Eq. 4 The final state 21 is subsequently post-processed (e.g., uniform resampling, mapping back to geographic coordinates, and trimming or interpolating to satisfy length priors), yielding the generated trajectory under the specified condition.
EXPERIMENTS
In this section, we evaluate TrajFlow to answer the following research questions: Q1: Does TrajFlow outperform baseline methods on key evaluation metrics? Q2: How well does Tra- jFlow perform in multi-scale trajectory generation? Q3: To what extent can TrajFlow reproduce trensportation-mode diversity? Q4: How efficient is TrajFlow in terms of training and inference?
5.1 SETTINGS
Dataset. We use the 2023 nationwide Blogwatcher dataset for Japan. This private dataset, provided by Blogwatcher Inc., contains fine tne-grained GPS records collected through multiple mobile applica- tions and comprises millions of trajectories. Each record includes anonymized user IDs, latitude, longitude, timestamps, and transportation modes.
Baselines. Diffusion-based methods represent the current state of the art in GPS trajectory genera- tion, and we adopt DiffTraj (Zhu et al. 2023h) as the representative diffusion baseline. In addition, we include TrajVAE (Chen et al.j 2021) l) and TrajGAN (Rao et al., 2020) as representative deep generative and adversarial baselines, respectively. To disentangle the contributions of the key com- ponents in TrajFlow, we further evaluate several ablated variants. w/o-FM: the CFM objective and ODE solver are replaced with standard DDPM denoising procedure. Because the performance of DDPM-style model is highly sensitive to the number of denoising steps, this comparison is reported separately under different step settings in Appendix B w/o-OD: the fine-grained OD prediction head, which predicts origin/destination coordinates within the conditioned OD zones, and the per- trajectory harmoniztiiorreconstttttoo pipeline are removed, so trajectories are generated directly in geographic space. w/o-RDP: the RDP parpettorryammmmizattiii step is omitted, and raw trajec- tories are fed into the model. We also evaluate the combined removal of RDP and OD prediction. These ablations isolate the effects of the flow-mate now-matching objective, the harmonizaaio/rrecossruciioo strategy, and the trajectoryccoppesssci step on fidelity and scalability.
Evaluation Metrics. We evaluate generation quality from two perspectives. Aggregated-levet The Jensen-Shamnon divergence of spatial density (density JS) measures how well synthetic data re- produces the population-leve geo- distrribbittton of movements. Trajectory-level: We assess trajec- tory similarity using Dynamic Time Warping (DTW) and the continuous Fréchet distance (Fr). DTW captures similarity under flexible alignment between trajectory points, whereas Fréchet distance is more sensitive to the overall geometric shape of the path. Together, they provide complementary evaluations of trajectory fidelity. For both metrics, report the median, and 10th/90th percentiles (P10/P90) to capture central accuracy and dispersion. Details are provided in Appendix A.1
5.2 EVALUATION
Overall Performance (Q1). Across spatial scales Central Tokyo (urban). Tokyo Metropolis (metro), and Japan (nationwide) the best-performing configurations consistently come from the TrajFlow family, rather than from diffusion or other deep generative baselines. The advantage is more moderate at the urban and metropolitan scales but becomes pronounced nationwide, highlight- ing stronger cross-scale generalization.
At the urban scale, although the full TrajFlow model achieves strong overall performance, the best results are obtained by TrajFlow-wad wwt---/w-RRDDDDD-- which remains within the flow-matching family. This suggests that when trajectories stay within a relatively homogeneous small-scale spatial range, directly generating raw coordinates may already be sufficient, and the additional RDP-based harmo- nizzaiion/rcoonstuuction is not always necessary.
At the metropolitan scale, several of the best indicators shift from RooFFlow-w/RRDP&&0 to Tra- jFlow- RDP, indicating that the OD-uuided harmonization and reconstruction component begins
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Table
Evaluation grouped by region (unit km)). Best metric in bold.
Method
Density IS
DTW not &. Fined 4 DT DTWpro
DTWps Frgg
Frpio & Fipep J
Coutral Tokyo
TrajFlow (ours)
0.0674
20.350
0.304
13,392
10:574
39.119
0.174
0.200
0.674
TraFFoowwhh www. wD
0.3560
916.436
13,862
708.183
432.567
1,740.890
7.313
7.064
20.858
TrajFlow-woo-BB
0.340
11.149
47.959
0.873
TrajFlow-woo RDP & OD
0.0323
8.179
0.184
4,586
4,994
14,189
0.118
0.110
0.363
DiffTraj
0,1340
44.321
0.651
40,713
19.399
109.349
0.544
0.341
1.774
TriGAN
119.230
1,288
TryVAE
0.1041
32.874
0.469
36.387
14.000
103.232
0.679
0.258
1.842
Tokyo Metropolis
TraFFlow (ours)
0,1239
18.167
0.335
16.892
7.678
44.316
0.333
0.130
0.933
TrgFFlow w/o. OD
0,1064
16.466
0.307
10.189
9.307
32.126
0.192
0.180
0.683
ItajHlowwwooRLD
0.1197
18.417
0.298
24.152
6.637
67.674
0.473
0.121
1.339
TrajFlow-woo RDP & OD
0.0800
14,416
0.303
7.684
8.659
23.978
0.176
0.592
DafTraj
0.2918
88.559
1.220
78.339
38.663
199.501
0.982
0.586
3.035
ToiGAN
0,3821
399
10.224
I, 184.077
155.40) 401
2,854.060
20.627
2,290
$1.389
TAaVAE
0.765
2.299
Japan nationside
TraiFlow (ours)
55.964
TrajFlow-wroOOD
0,4888
100.271
1.522
75.774
50.877
216.168
1.177
0.774
3.145
TragHoowwwo--HB
0,2734
24.690
0.400
27.928
9.047
92.641
0.511
0.156
1.699
TrajFlom-woo RDP & OD
0,4865
105.011
1.662
89.509
53.549
280.092
1,380
0.870
3.802
DifTTrij
0.6727
451.042
5.329
635.120
157.379
1,741 .025
6.973
1.915
18.924
TajGAN
0.5278
403.282
6.653
999.210
79.556
2,853.557
17.703
1.134
48.838
TroVAE
0.5228
135.377
2.216
236.143
28.394
577.139
3.884
0.435
9.919
show clear benefits as the spatial range increases. Meanwhile, TrajFlow maintains performance comparable to that at the urban scale.
At the nationwide scale, the advantage becomes substantial: DTW med 10.977, Frmed 0.192, tight IQR/P90, and the lowest density JS, while alternative methods exhibit much larger medians and heavier tails. Although TrajFlow not strictly the best on every metric smaller scales, the only method family that maintains a strong balance among shape fidelity, stability (IQR/P90), and spatial distribution (density JS) across all scales, and it clearly dominates in the nationwide setting.
Geographic visualizations are provided in Fig. 4 This pattern is consistent with the analysis in Sec. 4.1 when trajectories remain within relatively small spatial range, the SNR issue in DDPM less severe; however, under nationwide scale patterns are mixed-the scale mismatch in diffusion hinders performance across scales, limitation that flow matching addresses more effectively.
inveraaioonwhert urban-, metropolitan-, and nationwide-
Multi-scale Robustness (Q2). From the city level to metropolitan level and further to the nationwide level, Tra- jFlow maintains low median DTW/Fréchet values and rela- tively narrow dispersion while keeping density JS under trol. This result indicates that the model remains robust as the spatial range expands and the heterogeneity of trajectories in- creases. By contrast, diffusion-based generation becomes in- creasingly unstable when trajectory subsets span very differ- ent numerical ranges, from short local trips to long-distance nationwide movements. This observation is consistent with the analysis in Sec. [. the fxee-magnitude noising process DDPM introduces scale mismatch under multi-scale set- tings, whereas conditional flow matching learns a determin- istic transport field and avoids error accumulation along long denoising chains, leading to better robustness across heteroge- neous regions and transportation conditions.
Ground-Truth
Generation
Figure 5: Per-mode average trip distance in Tokyo: ground truth vs. generated.
Transportation-mode Diversity (Q3). Preserving the diver- sity of transportation modes as important as maintaining spa- tial fidelity in generative mobility models.
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Ground-truth
TrajFlow
B
DiffTraj
B
GAN
VAE
317
Figure 4: Visualization of trajectory samples. Ground-truth and generated nationwide trajectories shown with zoomed views highlighting three representative regions: (A) Tokyo Metropolis, (B) Tohoku Area, and (C) Kansai Area, across all generative models.
We evaluate this by comparing per-mode trip distance distributions of ground-truth and generated trajectories in Tokyo. As shown in Fig. [ the generated data matches the characteristic profiles of four representative modes, maintaining realistic differences in trip lengths. This indicates that TrajFlow not only captures spatial fidelity but also preserves transportation-modee diversity (see additional results Appendix C..
Training and Inference Efficiency (Q4). TrajFlow is optimized with the CFM objective, which requires only a single time step per sample, and generates trajectories by integrating the learned ODE with small fixed budget of about 10 steps. In contrast, DDPM performance is highly sensitive the number of denoising steps (see Appendix B) among the tested settings (10, 50, 100, 200, 300), the best trade-off between lensen-Shannon divergence and trajectory-shant fidelity typically appears near 200 steps, while 300 steps provide only marginal or inconsistent improvements at significantly higher cost. Notably, even with 300 steps, DDPM fails reach the performance of TrajFlow. These results highlight that competitive fidelity can be achieved by TrajFlow with far fewer steps (about 10) in both training and inference.
5.3 ABLATION STUDIES
w/o-FM: Replacing the CFM objective with DDPM-style denoising procedure yields monotonic but limited gains as the number of denoising steps increases, and consistently underperforms Tra- iFlow in DTW, Fréchet. and density JS even with large step budgets. This confirms flow matching as the main driver of fidelity and stability. w/o-RDP: Removing trajectory harmonization retains micro-jitter and redundant points, increasing Fréchet/DTW medians and tail metrics; the Japan

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split, it also raises density JS. Thus, RDP improves not only efficiency but also accuracy by sup- pressing noise and harmonizing sampling. w/o-OD: Dropping the OD predictor sometimes lowers density JS in small regions but consistently worsens DTW/Fréchet and dispersion, and degrades both shape and density metrics nationwide. w/o-RDP & OD: Combining both removals produces the greatest deterioration, underscoring their important role, particularly nationwide scale.
CONCLUSION
We introduced TrajFlow, flow-matching- based framework for generating pseudo-GPS trajecto- ries. By integrating trajectory harmonization and reconstruction into a conditional flow-matching generative framework, TrajFlow addresses key challenges in large-scale GPS trajectory genera- tion by maintaining robustness across spatial scales, preserving transportation-ne moode diversity, and achieving strong efficiency, with the clearest advantage at the nationwide scale. Evaluated on nationwide mobile-phone GPS dataset from Japan, TrajFlow or its variants outperform diffusion and other deep generative baselines. Particularly, it balances trajectory-shape fidelity, stability, and population-level spatial consistency across scales, achieves competitive accuracy with substantially fewer ODE steps.
Due to privacy constraints and data-access limitations, we focus GPS trajectory generation and do not use any per-user attributes (e.g., age, gender, home-work identifiers) or persistent pseudony- mous IDs, and thus the current model does not capture individual preferences. As future work, aim to extend TrajFlow from GPS trajectory generation to broader human mobility modeling while preserving privacy.
LLM USAGE STATEMENT
In accordance with the ICLR 2026 policy LLM usage, disclose that LLMS (specifically Ope- nAI's ChatGPT) were employed as a general-purpose writing assistant. The usage was limited to improving grammar, clarity, and LaTeX formatting of the manuscript.
ACKNOWLEDGEMENTS
This work supported by JSPS KAKENHI Grant Number 24K17367, JSPS KAKENHI Grant Number PP25211264 JSPS KAKENHI JP24K02996, and JST CREST JPMJCR2IM2 The authors would like thank Prof. Ryosuke Shibasaki, of The University of Tokyo and MocationMind Inc., for his support and guidance.
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A APPENDIX
A.1 EVALUATION METRICS
To quantify the fidelity of the generated trajectories, besides the use of density JS-divergence, we also employed two trajectory(line)-eeee evaluation metrics: DTW and Fréchet distance. DTW aligns trajectories time and is robust to local temporal shifts, highlighting point-wise spatiotem- poral fidelity. Fréchet distance, in contrast, evaluates the closest continuous matching of two curves and is more sensitive to global path geometry. Using both metries provides comprehensive view: DTW captures enn-graieed temporal accuracy, while Fréchet complements it by emphasizing over- all spatial shape consistency. The definitions are shown as follows:
Aggregated-level: Consen-Shannon (JS) Divergence of Spatial Density. Let p(s) and g(s) be the normalized 2-D spatial density maps (keree-smoothhed or mesh-count histograms) of the real and generated trajectories, respectively. The IS divergence is the symmetrized and smoothed version divergence:
respectcivi.
of the
JS(p ll q) = (L p+ + KL. 222).
(5)
where KL(pIlm) = Σ, p(s) log Mial This metric measures how well the synthetic data reproduces the population-level geographical distribution of movements; lower values indicate closer global density.
Trajectory-level: Dynamic Time Warping (DTW). Given two trajectories A = {ai.... } and = (b),..., .b,), where ds bj E I22 are latitude-longitude points, DTW finds an alignment path æ {(i,, ) with i f1 and iK = m, jk = n, that minimizes the cumulative
k==
Euclidean distance
DTW (A, B) min Σ
0ii
bj.
The alignment allows non-linear warping in the time dimension, making DTW robust to local speed or sampling differences and highlighting fine-grained spatiotemporal fidelity.
-raje:tory-level: Continuous Fréchet Distance. For the same curves A and interpreted as continuous functions a, B [0, R2 The Fréchet distance is
Fr(A, inf max [la()(t) - -
0,0 xE[0.1]
where & and ui range over all continuous, non-decreasing ce-parameteriizaioon. of [0, 1]. Intuitively, is the minimum leash length required for a person and a dog to walk along the two curves without backtracking. Unlike DTW, Fréchet does not explicitly align discrete time stamps; it captures overall geometric similarity and is sensitive to global path shape.
Summary of Usage. For every generated trajectory we compute DTW and Fréchet distances to its nearest ground-truth neighbor and report the median, and 10th/90th percentiles (P10/P90) to capture both typical accuracy and dispersion of errors across the distribution.
Fréchet distances capture geometric deviations, whereas DTW captures temporal misalignment. DTW explicitly aligns sequences the time dimension it penalizes trajectories that are spatially similar but temporally mismatched. Computing these metrics enables us to capture both geometry and temporal mismatching.
In addition, report P10 and P90 alongside the median to capture the model's robustness across the long-tailed complexity of human mobility: human mobility is usually long-tail, reporting only the Median (Central Accuracy) may mask model failures on complex outliers. By reporting P10/P90 (extreme/long tail case), we demonstrate that TrajFlow remains stable and accurate even for the tong-tail part trajectories, rather than just fitting the easy majority.
Together, JS divergence evaluates aggregated-lewe spatial consistency, while DTW and Fréchet jointly measure individual-patt fidelity from complementary temporal and geometric perspectives.
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A.2 DATA COMPRESSION ALGORITTMS
A.2.1 CANDIDATE ALGORIHTM
We evaluate seven representative parameterization haattaaammnizztiion) methods implemented in our codebase:
a) direct_k: Are-length reparameterization followed by uniform sampling of K points along [0, 1].
b) det: Discrete Cosine Transform (DCT-III) of the arc-length uninggt curve for zxt) and
v(); keep the first DCT M coefficients.
c) rdp.k: Ramer-Douggh Hamer-Douglas-Peuckke harmonization with a binary search on the tolerance so that the simplified polyline contains approximately К vertices; if necessary, linearly inter- polate to exactly K points.
d) anchor: Least- squares spline fitting with automatically detected "anchors" (including end- points) that receive a large weight Wanchor in the fitting.
e) spline Least-squares spline fitting with uniform weights (no anchors).
f) dct deviaatioon:: Take the straight line connecting start and end points as a baseline; apply DCT the perpendicular deviation sequence and retain 2K coefficients together with the endpoints.
g) complex Represent the curve as + iy, apply FFT, and keep the first K complex coefficients.
The RDP algorithm simplifies trajectory by recursively removing points that lie within distance threshold e of the line segment connecting their neighboring points, while preserving the essential geometric shape of the trajectory. Formally, given the ground-truth GPS trajectory dataset X (trjj, traje, .... traje on each trajectory traj = (l..4,..., (n) is processed as follows:
Algorithm Ramer- Douglas Peucker (RDP) Algorithm
1: function RDP(traj, c)
2: dmax <
3: inder
4: end + length(Iraj) -
5: for
to end do t perpendiiellaaDisttceemmmm line(traj0)) traj(end))
6:
7:
if d > dmaa then inder t- i. dmax t-
8:
9:
10: end if
11: end for
12:
if dmaa then
13:
resultsl < RDP(mrajO....ndd resull.s2 RDP( RDP(raajindde... linder. end).
14:
15:
return concatenate (0... - 1], results2)
else
17:
return
end if
19:
end function
A.2.2 EXPERIMENTS WITH DIFFERENT PARAMETERS
To evaluate the influence of trajectory-harmonizzee harmonization granularity, we compared seven parame- terization diriiidd-irree.... dct, rdp_k, anchor, spline.lsg, det.deviation and fft complex- under four target point budgets (K (5, 10, 20, 30}) - while the original length 120, representing compression ratios of approximately (4.2%, 8.3%. 16.7%, 25.0%) respectively.
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For each configuration report the mean Dynamic Time Warping (DTW) and Fréchet distance (Table ) and visualize qualitative differences in Figures. T
Overall, RDP-based simplification (rdp_k) consistently achieves the lowest trajectory-level errors, with average DTW decreasing from 2.77 at K==5 to se 0.59 at ==30, and Fréchet distance dropping from 0.058 0.015. The closely related spline least-squares (splimg lnn....... lsc) and DCT methods follow as the next best performers. Fourier-based fft_complex and deviation-only DCT are markedly worse, reflecting their sensitivity high-frequency noise.
Increasing the point budget unsurprisingly improves accuracy for all algorithms, but the gains ta- per beyond = DTW and Fréchet for róp_k improve only marginally from K=20 to =330. Visual inspection (Figures, 6 & 7 & & 9 confirms that K=10, i.c., 8.3% compression rate, al- ready captures the salient geometry of typical trajectories while preserving the strong compression benefits required for efficient training. Based on this analysis, we adopt RDP with K==10 as the default harmonization setting for TrajFlow, striking practical balance between trajectory fidelity and computational cost.
We highlight two necessities RDP in our tasks:
RDP used only dimensionalitt-reductiii method. We compress each trajec- tory (often around 120 points) into a smaller set of keypoints (around 10). This compact representation greatly improves fow-matching training efficiency and stability, especially across multiple spatial scales.
RDP provides the best balance between compression ratio and reconstruction accuracy. As shown in our ablation study, RDP achieves lower DTW and Fréchet distances than alter- natives such as DCT, spline fitting, or FFT. This ensures that the simplified representation maintains high spatial fidelity before the interpolation step.
Table 2: Reconstruction Performance (Avg DTW/Fréchet, unit=km). Best (lowest) values bold.
Param 5
Param 10
Param 20
Param 30
Method
Fréchet
DTW
Fréchet
Fréchet
Fréchet
direct
3.78
0.0430
0.0205
det
3.23
0.0814
1.24
0.0326
0.69
0.0150
0.61
0.0137
rdp.k
2.77
0.0580
0.95
0.0219
0.61
0.0143
0,59
0.0150
anchor
16.42
0.3333
1.75
0.0405
0.76
0.0191
0.61
0.0138
spline lsq
3.1
0.0665
1.22
0.0271
0.68
0.0150
0.61
0.0136
det_iivintion
4.66
0.0951
4.06
0.0874
0.0842
5.17
complex
24.11
0.5120
0.6054
0.6363
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431 400
Figure 6: Parameter Number =
Figure 7: Parameter Number 10
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40
Oggat
Figure 8: Parameter Number 20
Soal
Lrges
Lagan
Figure 9: Parameter Number 30
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B ADDITIONAL COMPARISON WITH DENOISING DIFFUSION MODELS
One possible concern is that diffusion models might achieve comparable performance to TrajFlow if trained or sampled with a larger number of steps, rather than using the same limited steps as in flow matching. Our experiments confirm that increasing the number of steps indeed improves performance; for instance, with 300 steps, diffusion models approach the performance of the pro- posed method, although they remain slightly inferior (Table 3) Notably, while further increasing the number of steps might eventually surpass TrajFlow, this underscores the key advantage of our flow-matching ter--mmttcinn-aaeeedd based approach: it achieves high fidelity while maintaining superior efficiency.
Table 3: TrajFlow-woo-M performance with different training/sampling steps (unit: km). Best
metric bold.
Method
Density IS
DTW J. Froat + Dr DTW 4
DTWpso J Frige Piyee Fryso
Tokyo
TrowFlow (ours)
0.0674
20.350
0.304
13,392
10.574
39.119
0.174
0.200
0.674
FrolFlowwwoo-Fh FM (step=110)
0.3213
362.611
5.844
794,886
86.305
2096.804
14.045
1.149
37.590
IrajFlow-w/ooFMM (steps=50)
0.2923
263,889
4,390
694.411
64.512
1827.793
12.156
0.855
32.903
TraiPlow-w/o-FN (steps= 100)
0.2269
(42.836
2.363
303,280
38.252
749.346
5.244
0.519
12.811
TrajFlow-wlo. FM FM (0tep=2000)
0.1208
36.434
0.583
49.489
15.035
130.881
0.975
0.247
2.437
TrajFlow-w/o-Fi (steps=300)
0.0807
24. 303
0.349
19.773
11.768
$7,728
0.331
0.211
1.049
Tokyo Metropolls
TrajFlow (ours)
0.1239
18.167
0.335
16.892
7.678
44.316
0.333
0.130
0.933
TrafFlow-w/o-H (step==10)
0.3833
7.668
994.283
154,963
2.069
TrojFlow-w/ooFM (stops=50)
0.3657
429.968
6.866
951,462
115,913
2935.618
16.754
1.555
50.237
TrajFlow-wlo-EM (steps=100)
0,3351
344.806
5.774
781.324
84.420
2006.533
13.825
1.118
36.338
TriiFlow-w/o-FM (steps=200)
0.2600
139.901
2.423
163.029
45,480
416,262
3.040
0.644
7.104
TrajFlow FM (stepe=300)
0.1690
33.035
0.546
34.456
11,806
84.754
0.653
186
1.527
Japan
TrawFlow (ours)
0,2270
10.977
0.192
18.221
3,984
55,964
0.361
0.072
1.119
TrajFlow-wlooFNh (stepo=10)
0.5808
495.961
7.901
969.033
166.495
3267.659
17.900
2.276
56.966
TrajFlow-woo-Hh (slep=500)
0.5632
367.991
5.821
738.327
117.033
2585.896
13.551
1.512
45.142
TrafFlow-w/o-FM (stcps=100)
0.5220
210.646
3.344
407.453
70.677
1332.320
7.386
0.996
23.968
TraiFlow-w/o-FM (0t)ps=200)
0.3856
55.417
0.847
88.626
19.797
263.442
1.619
0.311
4.622
TrajFlow-wloFFM (steps=300)
0.3047
26.125
0.412
36.912
9,376
113.981
0.700
0.151
2.094
Beyond the accuracy performance, we also compared the inference efficiency (time cost) between the proposed method and diffusion-based version (TrajFlow-w/o- shows, the flow matching based approach has a much higher efficiency than the diffusion-basee approach. Specifically, the diffusion- based version requires over 30x more inference time-cost while achieving accuracy levels that are comparable yet still lower than TrajFlow.
As Figure. [0 and Table.
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Inference time per trajectory (original labels)
Method
TrajFlow (ours)
TraFFlowwWe-FF (steps=10) 10)
TajFlooww/ooFFM (steps=50)
watilooww/o-fll (steps=100)
Tra
Seconds per trajectory
TrajFiowww/o-FF (stops-200) 200)
0.15
0.10
0.05
50
200
300
Sampling steps
Figure 10: Bar plot for time cost comparison in inference stage.
Table 4: Comparison table for time cost in inference stage.
Region
Method
Steps
Sec/Sample
Sampling Sec
Total Sec
Central Tokyo
TrajFlow
10
0.0097
0.9696
4.8912
Central Tokyo
TrajFlow-/oo-M (steps=10)
10
0.0100
1.0039
4.9646
Central Tokyo
TrajFlow-w/o-FTM (steps=50)
50
0.0382
3.8235
7.7105
Central Tokyo
TrajFlow-w/o-FTM (steps=100)
100
0.0761
7.6105
11.5326
Central Tokyo
TrajFlow-w/o-F (steps=200)
200
0.1585
15.8546
19.8442
Central Tokyo
TrajFlow-w/o-FM (steps=300)
300
0.2237
22.3682
26,3010
Tokyo Metropolis
TrajFlow
10
0.0097
0.9735
4.8695
Tokyo Metropolis
TrajFlow-w/ooFii (steps=10)
10
0.0135
1.3465
5.7994
Tokyo Metropolis
TrajFlow-w/o-FM (steps=50)
50
0.0474
4.7377
8.6324
Tokyo Metropolis
TrajFlowww/ooFF (steps=100)
100
0.0816
8.1608
12.1447
Tokyo Metropolis
TrajFlow-wwo-FIM (steps=200)
200
0.1474
14.7445
18.6668
Tokyo Metropolis
TrajFlow-w/o-FM (steps=300)
300
0.2356
23,5593
27.5961
Japan
TrajFlow
10
0.0086
0.8575
4.7650
Japan
TrajFlow-w/o-FM (steps=10)
10
0.0095
0.9466
4.8438
Japan
TrajFlow-w/o-FiM (steps=50)
50
0.0391
3,9072
7.8493
Japan
TrajFlow-w/o-FM (steps=100)
100
0.0860
8.6031
12.5301
Japan
TrajFlow-w/o-FM (steps=200)
200
0.1515
15.1521
19,0516
Japan
TraiFlow-w/o-FM (steps=300)
300
0.2240
22.4007
26.6460
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Published as a conference paper at ICLR 2026
C TRANSPORTATION-NODE DIVERSITY
Figures] and Figure 12 compare the generated trajectories of our model with the ground truth in four modes of transport. Mode diversity is much more pronounced within Tokyo, where travelers frequently switch among walking, cycling, buses, subways, private cars, and multiple rail systems. In contrast, on nationwide trips, mobility patterns are dominated by a much smaller of modes (primarily long-distanee trains), while local segments are typically sparse or not captured at the same granularity.
C.I URBAN-WIDE(TOKYO)
In the ground-truth data, distinct patterns emerge: train trips typically span larger spatial scales and extend to the outskirts of Tokyo; car trips are also long but more concentrated in central areas; bike and walk trips both cluster within local communities, though with different levels of continuity. These diverse modal behaviors are well reproduced by our model, demonstrating its ability to capture transportation-mont mode heterogeneity.
C.2 NATION- WIDE (JAPAN)
In the ground-truth data, we find that the train trajectories show more concentrate which is reasonable the choices for long- distancee railway network limited, and car trajectories show more diverse routes. Most walk and bike trajectories are limited in local area.
Tokyy
Takgo Area
WALK- Takyo
Tabyo Area
(a) Ground truth (Tokyo).
TRAIN Tokyya Area
CAR: Takkgo Arech
WALK Tokyo Aroa
RICP Tolyo Area
A.1
Loghon
Lorgl
(b) Generated (Tokyo).
Figure 11: Transportation-moode diversity visualization: GT vs. Gen in Tokyo.
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Published as a conference paper at ICLR 2026
Train
B
A
A
Car
B
A
B
Walk
B
Bike
B
(a) Ground-truth
Train
B
B
Car
B
Walk
B
Bike
B
(b) Generated
Figure 12: The capability to generate GPS trajectories under given transportation mode conditions. Ground-truth nation-wide trajectories shown with zoomed views highlighting three representative regions: (A) Tokyo Metropolis, (B) Tokaido Area, and (C) Kansai Area, across various transporta- tion modes: Train, Car, Walk, Bike (a) shows the ground-truth trajectories. (b) shows the generated.
22

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Published as a conference paper at ICLR 2026
D REPRODUCIBILITY
D.I DATASET INFORMATION
In accordance with the data policy of Blogwatcher Inc., the complete ground-truth BlogWatcher dataset can only be accessed through a strict application process. Although the dataset used in our study originates from a single data provider, is sourced from over 140 independent mobile applica- tions (as noted on http:///wwbbbwwwtchcc.o... www.wwatchhr.....pp/.
ensuring substantial diversity in data collection. Because comparable multi-scale datasets are not publicly available, we are unable benchmark TrajFlow on alternative nationwide or multi-level datasets. The dataset we used spans the period from January 2023 to December 2023 and contains approximately 3,000,000 (3 million) trajectories across Japan. For our experiments, we derive three subsets of different spatial scales: (1) Tokyo City, (2) Tokyo Metropolis, and (3) Nationwide.
uid
segment.id
model
mrods
time
lat
lon
STAY
STAY
2023/2/6 0:00
35.9497
139.5576
STAY
STAY
2023/2/6 0:15
35.9497
139,5576
2
MOVE
TRAIN
2023/2/6 0:36
36,2269
114,1721
MOVE
WALK
2023/2/6 0:39
36.7236
114,4598
Table 5: Example rows of the dataset used. (Note: this example data is only for showing data format without real lat/lon values.)
Each trajectory is pre-segmented according to transportation mode. The data fields relevant this study are summarized in Table 5 Here, uid denotes an anonymized user identifier, however, we do not utilize any user-level identifiers in this work to avoid potential privacy concerns. The field segment. id indexes individual trajectory segments; raan model distinguishes between STAY and MOVE states, and use only the MOVE segments. The field trans_ trans_mode2 provides fine- grained transportation modes such as TRAIN, CAR, WALK, and BIKE. Within movement segments, GPS points are recorded at an average interval of least one minute.
To validate our method in open source dataset, we additionally evaluate on two open-source datasets in Chengdu and Xi' an, see Section [E the Appendix. In addition, a portion of the processed demo data, together with the implementation and generated results, will be made publicly available upon acceptance of this work.
D.2 MODEL ARCHITECTURE
Backhone: We employ U-Net Architecture as the vector field estimator.
Dimensions: Base channels = 128. Channel multipliers [1, 2, 2,
Structure:
Two residual blocks per stage with SiLU activation. Attention mechanisms applied at resolution 16.
Embeddings: Timestep embedding dimension 512 (4x base channels). Hidden dimen- sion for condition embeddings is 512.
Conditioning (Wide & Deep): We utilize a "Wide & Deep" architecture encode heterogencous
inputs:
Wide Component: Linear projection of continuous features (e.g., speed, distance).
Deep Component: Categorical embeddings for Departure Time (288 bins), Ori- gin/Destination IDs, and Transportation Modes (5 classes).
Fusion: The outputs are fused into 22-diimnsionnl condition vector, which is injected into the U-Net residual blocks via cross-attention or additive projection.
D.3 TRAINING CONFIGURATION
Optimizer: Adam optimizer (B1 0.9, 32 00.999 with weight decay.
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Published as a conference paper at ICLR 2026
Learning Rate: Initial learning rate set to 1 x 10-4. We use ReduceLROnPLateen scheduler (factor=0.5, patience=200) monitoring validation loss.
Batch Size: 256 trajectories per GPU.
Training Budget: Up 500 epochs with Early Stopping (patience=5000 steps, delta=le"9)
Regularization: We apply random condition dropout (Classifier-Free Guidance) during training to prevent overfitting and enable guidance during inference.
D.4 ALGORITHM SETTINGS
Trajectory Harmonization (RDP): We use the Ramer-Douglas- Pouulas-PPeuckr (RDP) algorithm for compression.
Target keypoints M 10.
Epsilon tolerance determined via binary search (Ezol = 1e=5).
Max sequence length Imaz 120.
Flow Matching Solver:
Method: Euler ODE integrator.
Inference Steps: 10 steps (step size = 0.1). This setting was chosen to balance fidelity and efficiency (approx. 0.01s per sample).
Diffusion Baseline (for comparison): Linear schedule (1e-6 to 5e 5e DDIM sampler used with steps ranging from 10 300 for efficiency benchmarking.
D.5 COMPUTING ENVIRONMENT
All experiments were implemented in PyTorch and executed on a cluster of four NVIDIA RTX
6000 Ada GPUs (40GB memory each). The software environment includes CUDA 12.6 and Python 3.9.
E VALIDATION ON OPEN-SOURCE DATA
We report the results based on 1,000,000 trajectory samples for each city. For reference, the previous DiffTraj paper reported using 3,493,918 trajectories from Chengdu and 2,180 28104834 trajectories from Xi' an. Across both cities, TrajFlow maintains strong performance and exhibits trends consistent with our main results (see Table. ())
Table 6: Evaluation grouped by region (unit = km). Best metric in bold.
Method
Density IS & DTTW and J. Fraet DTWWoR J DTWPi DTW J. Froo Firoo 4 Fryeo
Chengdu
TrajFlow (ours)
0.211 0.0809
35.911
0.547
29.418
15.839
72.048
0.392
0.279
0.959
TrofFlow-llo-OD
3.696
0.123
2.847
2.180
8.904
0.117
0.0614
TrolFlow-woo RDP
0.206
34.687
0,540
30.020
14.650
69.999
0.383
0.266
0.957
TrllFlow-wlo RDP OD
0.0140
2.158
0.0525
0.896
1.519
3.278
0.0243
0.0354
0.0880
TrajFlow-wlo
low-ooow OD Hoow
0,0811
3.724
0.123
2,800
2.142
8.844
0.119
0.0618
0.365
TrajFlloww// w/o RDP & Flow
0.203
36.166
0.561
30.311
15.213
73.719
0.388
0.276
0.985
DiffTraj (baseline)
0.0224
3.524
0.0944
1.563
2,312
5.460
0.0482
0.0606
0.161
XiAn
TrajFlow (ours)
0.284
43.457
0.564
35.390
16.948
79.586
0.379
0.277
0.897
TraiFlowwwlo-OD
0.0820
2.565
0.0842
2.009
1.530
8.488
0.116
0.0453
0.395
TrolFlow-wlo RDP
0.278
40.859
0.549
34.013
15.547
75.445
0.380
0.259
0.875
TrajFlow wia RDP OD
0.00556
1.111
0.0279
0.401
0.805
1.611
0.0120
0.0192
0.0443
wooo Flow
Tro/Flow-wlo OD & Flow
0.0819
2.354
0.0833
2.115
1.387
8.162
0.119
0.0448
0.395
TrajFlow-wlo RDP & Flow
0.278
40.328
0.555
33.247
13.592
75.524
0.382
0.257
0.822
DiffTraj (baseline)
1.154
0.0284
0.494
0.773
1.750
0.0132
0.0193
0.0466
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Published as a conference paper at ICLR 2026
F DISTINCTION FROM EXISTING APPROACHES
Our work introduces several key contributions that differentiate TrajFlow from existing trajectory- generation approaches:
First flow-matching model for GPS trajectory generation (methodological novelty). Prior trajectory-generaiinn methods-inclluing recent diffusion-based models-rely on stochastic reverse-time SDE sampling and require tens to hundreds of denoising steps. In contrast, TrajFlow is the first model to apply the fltchngt paradigm to GPS trajectory generation. Moreover, architecture tailored for flow matching, enabling the model to better handle spatial hetero- geneity and further improve generation performance.
introduce trajectory normalization scheme and specialized
First nationwide-scale, multi-geospatial-leee GPS generator pproblem-lever novelty). Existing models are restricted to small urban or single-city settings due to spatial het- erogeneity and instability. TrajFlow is the first model evaluated urban, metropolitan, and nationwide scales, trained on millions of mobile-phone GPS trajectories across Japan, demonstrating robust generalization across heterogeneous regions.
G PRACTICAL APPLICATION
TrajFlow handles variable-length trajectories through a conditioningrreconsssncciii strategy rather than asking the generative model to infer sequence length implicitly.
Fixed-length representation during training (Section 4.4). stable batch training under flow matching. all trajectories are represented using a fixed maximum length with padding and validity masks. This allows the model to learn continuous spatial dynamics without being affected by sequence-length variability.
Explicit duration conditioning (Section 4.3). The model is conditioned on Travel Time and Departure Time, which provide explicit temporal context. Because trajectory duration is given as a conditioning variable, the model does not need to guess estimate the temporal length.
Length-consiste reconstruction inference. generation time, the model predicts the spatial shape of the trajectory (via harmonized RDP points). The final trajectory is then reconstructed to the target duration using the provided Travel Time condition, ensuring that generated samples match the desired temporal length-whether 10 minutes or 2 hours.
This strategy enables TrajFlow to robustly generate trajectories with diverse and accurate temporal lengths while retaining stable training process.
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Published as a conference paper at ICLR 2026
H PRIVACY ISSUE
The inputs to our model are limited to departure time, origin-destination (OD) zones, and trans- portation mode, all of which are high-level, aggregated attributes that do not include or reveal any user-level identifiers (e.g., user IDs, device IDs, or fine-grained personal metadata). Therefore, the model is not exposed to information that could directly compromise individual privacy.
MEMORIZATION RISKS
TrajFlow designed learn underlying mobility patterns (e.g.. road network constraints, route choice) rather than memorizing specific coordinate sequences. Similar to tatuusiionnlo-matthiie models in computer iision-whie learn the concept of an object rather than copying specific train- ing images- our model generates trajectories by transforming Gaussian noise under OD and time conditions. The flow-matching process injects noise and learns a continuous probability flow from noise to data, making the generation inherently stochastic. As result, each sample starts from dif- ferent noise seed, and even with identical OD/time conditions, the model produces diverse and novel trajectories rather than retrieving or replicating any stored instance. This stochasticity, in models like Stable Diffusion, ensures diversity and prevents deterministic copying of training trajectories.
In addition, to explicitly prevent the model from "memorizing" specific conditional mappings (over- fitting), we apply Classifier-Fre: Guidance (CFG) and dropout trick, which consists of a training regularization and an inference mechanism: Training (Condition Dropout): During training, domly mask the input conditions (OD/Time/Men (iDe/////od///c... with a probability. This acts as a strong reg- ularizer, forcing the model to learn the general, unconditional distribution human mobility rather than relying on specific conditions to retrieve stored instances. Inference (Guidance Formula); Dur- ing generation/inference. we compute guided update using a weighted linear combination of the conditional and unconditional vector fields. This is the standard classifier-ff guidance formula, which increases the model's sensitivity to the conditioning signal without causing the model to memorize specific condition-traecctory pairs. By adjusting the guidance weight, we can strengthen or relax condition adherence, enabling higher-quality and non-deterministic trajectory samples un- der the same conditions.
ran-
Third, empirically, we observed that the minimum DTW distances between generated samples and the training set consistently non-zero. And even with the same condition, various routes could be generated.
J ETHICS STATEMENT
This work adheres to the ICLR Code Ethics. All experiments were conducted on anonymized, large-scale mobile phone GPS trajectory data, which was used strictly in aggregated form and under strict privacy rules. No personally identifiable information (PII) or user-level attributes (e.g., age, gender, home-work identifiers, or persistent pseudonymous IDs) were accessed utilized. Conse- quently, the model does not attempt to capture or infer individual preferences.
The proposed methods are designed to generate pseudo-GPS trajectories for research on mobility modeling and transportation systems, not to reconstruct or deanonymize individual user behavior. The use of RDP-based harmonization and OD-prediction modules focused on improving compu- tational efficiency and trajectory-level fidelity. without compromising privacy.
We acknowledge that trajectory data can be sensitive, and inappropriate applications may raise con- cerns around surveillance or discriminatory use. To mitigate this, we limit our study to method- ological contributions and evaluation on aggregated data. Our scope is restricted to GPS trajectory generation (sequences of locations over time), rather than full human mobility modeling that would include activity semantics, trip-chain structure, or purpose-specific constraints.
We believe this research can benefit society by enabling scalable simulation tools for urban planning, transportation analysis, and disaster response, while respecting user privacy. All legal, ethical, and research integrity requirements have been followed in the preparation of this work.
26


Reviews:
[{"review_id": "dHwixCJVre", "reviewer": "Reviewer_CQzo", "summary": "The paper proposes a new generative model for GPS trajectories of human mobility. The architecture is based on flow-matching. The GPS trajectories are first normalized and then simplified to both help with efficiency and training stability. The model is shown to outperform state-of-the-art models across both trajectory-level and aggregate-level evaluation measures.", "questions": "1. How are departure times, OD pairs, and transportation modes obtained in practice?\n2. Could you elaborate on why TrajFlow-w/o RDB & OD shows strong performance on the Central Tokyo region?\n3. Is there a risk that the model has memorized the training set? The reported DTW is the average across multiple generated trajectories, but what is the smallest value you have observed for individual trajectories?", "limitations": "", "rating": 10, "confidence": 5, "soundness": 4, "presentation": 4, "contribution": 4, "strengths": "1. Very strong performance for trajectory generation at nation-level scale\n2. The ablation study not only shows the importance of each part, but also discusses some of the inherent limitations of using a global coordinate frame when generating trajectories, which is that it introduces the risk of small details being lost when different trajectories have different scales.\n3. Provides new insights into what is important for generating trajectories: trajectory simplification, normalization, and flow matching are all critical components.", "weaknesses": "1. All results are based on a single dataset, which is not publicly accessible.\n2. Auxiliary data is required to sample from the model: departure times, OD pairs, and transportation modes. \n3. Limited discussion around the risk of memorization. The DTW measure shows the average DTW distance to the closest real trajectory. While achieving a low score might seem positive, it could also indicate that the model has learned to copy the training set, potentially increasing the risk of leaking private information. This can also lead to inflated evaluation scores, as copying training data can improve evaluation metrics without the model genuinely learning to generate novel trajectories.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "OusTmlgfa7", "reviewer": "Reviewer_577e", "summary": "This paper addresses the problem of pseudo-GPS trajectory generation, which is challenged by issues of spatial scalability, multi-modal transportation diversity, and generation efficiency. To tackle these limitations, the authors propose TrajFlow, a novel flow-matching-based generative framework that incorporates trajectory harmonization and reconstruction within a conditional generative paradigm. Experimental results demonstrate the effectiveness of the proposed method.", "questions": "Q1: Missing Figure and Table References: Some figures (e.g., Figures 1 and 3) and tables (e.g., Table 1) are not referenced, which affects readability. \n\nQ2: ODE is missing citation.\n\nQ3: The methodology section is somewhat difficult to follow. For instance, it is unclear where is  Figure 3 referred and how it aligns with the overall model design. It is better to give more discussions.\n\nQ4: Why are these evaluation metrics chosen? What is the rationale for using P10/P90 to describe central accuracy and dispersion?", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "S1. This paper studies the problem of pseudo GPS trajectory generation, which seems interesting. \n\nS2. The paper presents the first flow-matching-based generative framework.\n\nS3. Experiments show that the proposed TrajFlow outperforms the existing baselines.", "weaknesses": "W1. Novelty: The paper would benefit from a deeper discussion clarifying the differences between the proposed approach and more recent baselines.\n\nW2. Datasets: Experiments are conducted on only one dataset, which limits the generalizability of the conclusions. It is recommended to include additional commonly used datasets such as Chengdu and Xi’an to strengthen the empirical validation.\n\nW3.Baseline: The baselines used for comparison (from 2020, 2021, and 2023) are relatively outdated. The paper should include more recent baselines mentioned in the related work section and existing work such as Diffusion-TS to ensure a fair and comprehensive comparison.\n[1] Interpretable Diffusion for General Time Series Generation, ICLR 2024.\n\nW4. Lack of Complexity Analysis: The paper does not provide a theoretical analysis of time and space complexity. Including such analysis would help readers better understand the computational efficiency and scalability of the proposed framework.\n\nW5. Reproducibility: The paper lacks the codes, which may hinder reproducibility.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "9ygP23ZEjI", "reviewer": "Reviewer_P2bz", "summary": "This paper presents a novel high-fidelity GPS trajectory generation model, called TrajFlow, which aims to address key challenges in current research. Although real GPS data is highly valuable, its application is hindered by privacy concerns, high costs, and access restrictions. Existing generation methods based on diffusion models have high fidelity but suffer from three major limitations: they are limited to small urban areas, lack diversity in multi-traffic patterns, and are inefficient in terms of training and inference. The TrajFlow applies the flow-matching paradigm to GPS trajectory generation. The core of the approach is to address the signal-to-noise ratio collapse problem encountered by diffusion models when scaled to large scales. It achieves this goal through a trajectory coordination and reconstruction strategy: the trajectories are first compressed using the RDP algorithm and then normalized to a uniform feature space for training. Experiments on a nationwide GPS dataset covering the entire country of Japan demonstrate that TrajFlow outperforms baselines, such as diffusion models, at city, metropolitan area, and nationwide scales, while maintaining the diversity of traffic patterns and being highly efficient.", "questions": "1. How does this paper deal with the problem of variable-length generation of data?\n2. If the RDP algorithm is used to extract keypoints, it would hold the spatial characterization. So what is the difference between a trajectory generated using TrajFlow and one we interpolate directly based on keypoints?", "limitations": "", "rating": 6, "confidence": 5, "soundness": 3, "presentation": 4, "contribution": 4, "strengths": "1. This paper presents the first application of the flow-matching paradigm to the task of GPS trajectory generation, which addresses the problem that the performance of existing models, especially diffusion models, degrades dramatically when scaling from small urban scales to regional or national scales.\n2. TrajFlow is much more efficient than the computationally expensive diffusion model, which requires a large number of sampling steps. TrajFlow achieves high fidelity in generation with only about 10 ODE steps.\n3. TrajFlow overcomes the limitations of previous studies that are mainly limited to cab trajectory data, and is able to generate trajectories for multiple modes of transportation, including trains, cars, bicycles, and walking.", "weaknesses": "1. This paper lacks some details about the reproducibility of the models and algorithms, such as model architecture, parameter settings, code, algorithm process, etc.\n2. This paper uses trajectory data with multiple travel modes and a national scale. However, it's not publicly available, and the authors do not present many details about the dataset. This limits the reader's ability to review the technical performance of this paper in depth.\n3. The main evaluation metrics of the paper are biased towards space rather than time, such as DTW and Fréchet distance. These metrics are well-suited to measure the geometric similarity of two curves, but are limited in their ability to assess the temporal fidelity of trajectories.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "eGFZaANFsX", "reviewer": "Reviewer_vidk", "summary": "This paper introduces TrajFlow, a flow-matching-based generative model for synthesizing pseudo-GPS trajectories at a nationwide scale. Addressing key limitations of diffusion-based methods—namely poor scalability, limited transportation-mode diversity, and high sampling cost—TrajFlow integrates a trajectory harmonization and reconstruction pipeline with conditional flow matching. It is evaluated on a large-scale mobile GPS dataset from Japan and demonstrated superior performance.", "questions": "Q1: How does TrajFlow perform on non-Japanese datasets, particularly in countries with less structured transportation networks?\n\nQ2: Could the authors provide a more detailed comparison of training/inference time and memory usage versus diffusion-based models?\n\nQ3: What are the potential risks of model misuse, and have any safeguards been considered to prevent re-identification or surveillance applications?\n\nQ4: Why was RDP chosen over other curve simplification methods (e.g., spline fitting) in the final model, given that some alternatives performed similarly in the appendix?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "S1: It is the first application of flow matching to trajectory generation; novel integration of RDP-based harmonization and OD-conditioned normalization.\n\nS2: Strong empirical performance across multiple scales and modes; comprehensive ablation studies validate design choices.\n\nS3: Well-organized structure; clear problem motivation and contribution statement.", "weaknesses": "W1: The model is trained and evaluated only on Japanese data; it is unclear how well it generalizes to other countries with different urban structures or mobility patterns.\n\nW2: While the paper claims efficiency gains, runtime and memory usage are not compared in detail with baselines (e.g., training time, GPU hours).\n\nW3: Although privacy is discussed, the paper does not explore potential misuse scenarios (e.g., synthetic data used to infer real user behavior or re-identification risks).\n\nW4: The evaluation focuses on Tokyo for mode diversity; nationwide mode-specific performance is not as thoroughly analyzed.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)