ConvDiff: Multi-scale spatio-temporal convolutional networks with latent diffusion models for dynamic system modeling

In the modeling of spatio-temporal dynamic systems, tasks such as fluid dynamics, weather forecasting, and traffic flow prediction face highly complex spatio-temporal dependencies and nonlinear dynamics. These characteristics make it challenging for traditional physical models and data-driven methods to balance accuracy and computational efficiency. To address these challenges, we propose a multi-scale spatio-temporal convolutional network named ConvDiff, optimized specifically for dynamic system modeling tasks by integrating a latent space denoising diffusion model. ConvDiff effectively captures complex spatio-temporal features and handles uncertainties in physical systems by introducing multi-scale convolutional modules combined with a physics-guided diffusion mechanism. Specifically, our model incorporates eight temporal modules and four spatial modules, using a hierarchical convolutional and diffusion structure to capture the intricate dynamics of physical systems. The experiments involved different spatio-temporal data, such as those from TaxiBJ and the Navier-Stokes dataset. According to the findings, ConvDiff demonstrates substantial improvements in essential performance indicators. For example, in the TaxiBJ dataset, ConvDiff obtained a mean squared deviation of 0.29 and a PSNR value of 40.31, outperforming the best-performing models. Moreover, on the Navier-Stokes dataset, ConvDiff reduced the MSE by 51.15% compared to the best baseline model. These results indicate that ConvDiff effectively captures complex spatio-temporal dependencies and improves prediction accuracy, particularly in physics-driven dynamic systems. Our code is available at https://github.com/Ray-zyy/ConvDiff.