TRACE: Trajectory Recovery with State Propagation Diffusion for Urban Mobility

Jinming Wang; Hai Wang; Hongkai Wen; Geyong Min; Man Luo

cs.LGMar 19, 2026

TRACE: Trajectory Recovery with State Propagation Diffusion for Urban Mobility

Authors: Jinming Wang, Hai Wang, Hongkai Wen, Geyong Min, Man Luo

Organizations: University of Exeter Department of Computer Science Exeter, United Kingdom · Jingdong Logistics Beijing, China · University of Warwick Department of Computer Science Coventry, United Kingdom

Abstract

High-quality GPS trajectories are essential for location-based web services and smart city applications, including navigation, ride-sharing and delivery. However, due to low sampling rates and limited infrastructure coverage during data collection, real-world trajectories are often sparse and feature unevenly distributed location points. Recovering these trajectories into dense and continuous forms is essential but challenging, given their complex and irregular spatio-temporal patterns. In this paper, we introduce a novel diffusion model for trajectory recovery named TRACE, which reconstruct dense and continuous trajectories from sparse and incomplete inputs. At the core of TRACE, we propose a State Propagation Diffusion Model (SPDM), which integrates a novel memory mechanism, so that during the denoising process, TRACE can retain and leverage intermediate results from previous steps to effectively reconstruct those hard-to-recover trajectory segments. Extensive experiments on multiple real-world datasets show that TRACE outperforms the state-of-the-art, offering $>$ 26% accuracy improvement without significant inference overhead. Our work strengthens the foundation for mobile and web-connected location services, advancing the quality and fairness of data-driven urban applications. Code is available at: https://github.com/JinmingWang/TRACE

Figures & tables

Figure 1. The trajectories collected from mobile edge devices are usually irregular and sparse, which fail to precisely describe the behavior of moving agents, thus cannot be used in data-driven applications. Irregular and sparse trajectories cannot be used in downstream data-driven applications, such as route planning, traffic managing, logistics and delivery applications.

Figure 2. TRACE Framework. (a) Merge querying timestamps into observed timestamps in chronological order. (b) Initialize missing points with Gaussian noise. (c) Prior knowledge are included to explicitly tell the model where to recover. (d) The embedding of multi-modal contextual information. (e) The denoising process with SPDM that generates the dense trajectory. TRACE first embeds all contextual data, then aggregate them into a single input tensor, finally underwent denoising process, which produces the dense and regular trajectory.

Figure 3. The architecture of the modified UNet (upper, red) and the proposed MCGRU (lower, green). In the proposed UNet architecture, each UNet stage takes state features as an additional input, then produces the processed state features, which serve as the input for the next denoising step.

Figure 4. Three ways of batch management. Top: Shared $t$ among all samples in a batch. Middle: Different $t$ for each sample with little offset. Bottom: Uniformly distributed $t$ over the range $[1,T]$ . A single data sample (trajectory) will be used many times consecutively, if we load the entire batch of data with the same $t$, the model training become unstable. In contrast, try to make $t$ evenly distribution among data samples in a batch is better. — Figure 4. Three ways of batch management. Top: Shared $t$ among all samples in a batch. Middle: Different $t$ for each sample with little offset. Bottom: Uniformly distributed $t$ over the range $[1,T]$ . A single data sample (trajectory) will be used many times consecutively, if we load the entire batch of data with the same $t$ , the model training become unstable. In contrast, try to make $t$ evenly distribution among data samples in a batch is better.

Metric	Method	Dataset
Metric	Method	Xi’an	Chengdu	Logistics
MSE $\downarrow$	DeepMove	5.297	26.857	30.060
( $\times 10^{-3}$ )	AttnMove	0.068	0.234	3.201
	PriSTI	0.019	0.292	2.206
	DT + RP	0.326	6.919	4.250
	TRACE w/o SPDM	0.017	0.202	2.025

Table 1. The overall comparisons of six models with three metrics on three dataset. The trajectory length is 512 points, with 50% GPS points erased and the models are asked to recover the erased points.

Figure 5. The trend of recovery errors as the trajectory gets more irregular in terms of spatial and temporal distributions. There are breaks in y-axis because the magnitude of MSE differs a lot for different methods. Tested on Xi’an with 70% points erased and trajectory length of 512 points. The proposed model shows the best scalability as the trajectory gets more irregular in terms of spatial and temporal distributions.

Figure 6. The comparison among sparsity levels and trajectory lengths. The proposed model (with SPDM) shows the best robustness across different trajectory lengths and sparsity levels.

Method	Steps	Time	MSE	NDTW	MAE
Method	Steps	(s)	$\times 10^{-3}$	$\times 10^{-3}$	$\times 10^{-3}$
	500	119.176	0.0432	2.01	3.068
DDIM	51	12.36	0.0349	2.868	2.221
	26	6.65	0.0351	2.897	2.239
	11	3.18	0.0490	3.083	2.365
DDIM	500	129.57	0.0356	2.750	2.502

Table 2. The comparison of recovery time and quality with and without state propagation pipeline. Tested on Xi’an with 70% points erased and trajectory length of 512 points.

Method	Parameters	MACs	FLOPs
TRACE	6.28M	1.13G	2.28G
TRACE w/o SPDM	6.17M	0.99G	2.01G
DT + RP	9.10M	0.63G	1.27G
PriSTI	7.32M	3.24G	6.51G
AttnMove	8.15M	3.94G	7.92G
DeepMove	10.11M	1.94G	9.93G

Table 3. The number of parameters, multiply-accumulate operations (MACs), and floating point operations (FLOPs) of all methods.

Panel of Figure 7 — Figure 7. The comparisons among: (a) Number of denoising steps included in single training iteration. (b) Three ways of batch managing introduced in Fig 4 . Tested on Xi’an with 70% points erased and trajectory length of 512 points. The number of denoising steps included in a single training iteration has very little effect on final performance. While the proposed batch management algorithm is necessary for a stable training and significantly reduces loss.

	Average Speed	Moving Distance
	(m/s)	(km)
Ground Truth	1	1
Sparse Traj	0.6180	0.5788
Recovered Traj	0.8252	0.8480

Table 4. The moving speed and distance estimations computed from trajectories after normalization.

Panel of Figure 8 — Figure 8. The dataset of: (a) Dense trajectories as ground truth. (b) Trajectories with the same sparsity as usual logistics scenario. (c) Recovered trajectories using TRACE. The trajectories recovered by the proposed method makes sparse trajectory usable, and looks similar to ground truth.

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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 and 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.

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