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arXiv · 2512.04385

STeP-Diff: Spatio-Temporal Physics-Informed Diffusion Models for Mobile Fine-Grained Pollution Forecasting

Nan Zhou·Weijie Hong·Huandong Wang·Jianfeng Zheng·Qiuhua Wang·Yali Song·Xiao-Ping Zhang·Yong Li·Xinlei Chen
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Abstract

Fine-grained air pollution forecasting is crucial for urban management and the development of healthy buildings. Deploying portable sensors on mobile platforms such as cars and buses offers a low-cost, easy-to-maintain, and wide-coverage data collection solution. However, due to the random and uncontrollable movement patterns of these non-dedicated mobile platforms, the resulting sensor data are often incomplete and temporally inconsistent. By exploring potential training patterns in the reverse process of diffusion models, we propose Spatio-Temporal Physics-Informed Diffusion Models (STeP-Diff). STeP-Diff leverages DeepONet to model the spatial sequence of measurements along with a PDE-informed diffusion model to forecast the spatio-temporal field from incomplete and time-varying data. Through a PDE-constrained regularization framework, the denoising process asymptotically converges to the convection-diffusion dynamics, ensuring that predictions are both grounded in real-world measurements and aligned with the fundamental physics governing pollution dispersion. To assess the performance of the system, we deployed 59 self-designed portable sensing devices in two cities, operating for 14 days to collect air pollution data. Compared to the second-best performing algorithm, our model achieved improvements of up to 89.12% in MAE, 82.30% in RMSE, and 25.00% in MAPE, with extensive evaluations demonstrating that STeP-Diff effectively captures the spatio-temporal dependencies in air pollution fields.

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Nan Zhou, Weijie Hong, Huandong Wang, Jianfeng Zheng, Qiuhua Wang, Yali Song, Xiao-Ping Zhang, Yong Li, Xinlei Chen. 2025-12-04. STeP-Diff: Spatio-Temporal Physics-Informed Diffusion Models for Mobile Fine-Grained Pollution Forecasting. https://arxiv.org/abs/2512.04385

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