Diffusion for Diffusion: A versatile multiphysics fields refinement framework in pollutants transportation.

Refining coupled multiphysics fields in pollutant transport from sparse measurements is critical for environmental risk assessment and industrial pollution mitigation. However, existing numerical solvers and machine learning architectures exhibit inherent limitations in computational efficiency, generalizability, and predicting accuracy. To address these limitations, we present a diffusion-model-based deep learning framework. The target problem involves pollutant diffusion driven by coupled concentration and temperature gradients, examined in both two-dimensional transient and three-dimensional steady-state scenarios. Our approach integrates a physics-informed, equation-constrained scheme with a conditional diffusion model, enabling accurate recovery of high-dimensional spatiotemporal fields from limited observations. To validate the proposed method, we construct benchmark datasets using high-fidelity finite element simulations and double-color siren imaging under varied source distributions and boundary conditions. Quantitative evaluations demonstrate that our framework consistently outperforms state-of-the-art baselines-including ResNet, Transformer, and Fourier Neural Operator-in terms of super-resolution accuracy and robustness. These results suggest that the proposed approach offers a promising pathway toward real-time monitoring and analysis of pollutant transport in both environmental and industrial contexts.