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

arXiv: https://arxiv.org/abs/2512.04385 · HTML: https://mlsanity.com/paper/2512.04385/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 22 of its 59 references that are in the map.
- First posted on arXiv 4 Dec 2025.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 22 of 22)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [A Physics-informed Diffusion Model for High-fidelity Flow Field Reconstruction](https://mlsanity.com/paper/2211.14680/) (2022)
- [Spatio-Temporal Graph Neural Networks for Predictive Learning in Urban Computing: A Survey](https://mlsanity.com/paper/2303.14483/) (2023)
- [DiffusionPDE: Generative PDE-Solving Under Partial Observation](https://mlsanity.com/paper/2406.17763/) (2024)
- [FineMoGen: Fine-Grained Spatio-Temporal Motion Generation and Editing](https://mlsanity.com/paper/2312.15004/) (2023)
- [UniST: A Prompt-Empowered Universal Model for Urban Spatio-Temporal Prediction](https://mlsanity.com/paper/2402.11838/) (2024)
- [ClimODE: Climate and Weather Forecasting with Physics-informed Neural ODEs](https://mlsanity.com/paper/2404.10024/) (2024)
- [AirFormer: Predicting Nationwide Air Quality in China with Transformers](https://mlsanity.com/paper/2211.15979/) (2022)
- [Spatio-temporal Diffusion Point Processes](https://mlsanity.com/paper/2305.12403/) (2023)
- [UrbanVideo-Bench: Benchmarking Vision-Language Models on Embodied Intelligence with Video Data in Urban Spaces](https://mlsanity.com/paper/2503.06157/) (2025)
- [AirPhyNet: Harnessing Physics-Guided Neural Networks for Air Quality Prediction](https://mlsanity.com/paper/2402.03784/) (2024)
- [GinAR: An End-To-End Multivariate Time Series Forecasting Model Suitable for Variable Missing](https://mlsanity.com/paper/2405.11333/) (2024)
- [Deep Air Learning: Interpolation, Prediction, and Feature Analysis of Fine-grained Air Quality](https://mlsanity.com/paper/1711.00939/) (2017)
- [Spatio-Temporal Dynamic Graph Relation Learning for Urban Metro Flow Prediction](https://mlsanity.com/paper/2204.02650/) (2022)
- [Path Generation for Wheeled Robots Autonomous Navigation on Vegetated Terrain](https://mlsanity.com/paper/2306.08977/) (2023)
- [Ultra-High-Frequency Harmony: mmWave Radar and Event Camera Orchestrate Accurate Drone Landing](https://mlsanity.com/paper/2502.14992/) (2025)
- [TransformLoc: Transforming MAVs into Mobile Localization Infrastructures in Heterogeneous Swarms](https://mlsanity.com/paper/2403.08815/) (2024)

## Abstract (arXiv)

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.