New Diffusion Model Improves High-Resolution Data Assimilation

A novel data assimilation framework, named Iterative Refinement (IR), has been introduced to address the challenge of reconstructing high-resolution physical states from limited, low-resolution observational data. This is a critical problem in scientific machine learning, where traditional methods often require costly high-resolution forecast models or lack the ability to fully leverage past state constraints. IR innovatively decomposes the super-resolution task into a series of resolution-wise forecast-analysis operations across a multiresolution hierarchy. It employs a shared neural operator to provide a dynamic prior at each stage, while a conditional diffusion corrector refines the coarser-resolution state into a finer-resolution posterior. This iterative process allows for a more comprehensive exploitation of temporal information and generative capabilities. Evaluations on complex systems, including one-dimensional Burgers dynamics and two-dimensional Kraichnan turbulence, demonstrate IR's superior performance. Notably, it achieved significantly better accuracy on the challenging Kraichnan benchmark compared to several established super-resolution and data assimilation techniques, highlighting its advantage in strongly multiscale and underdetermined scenarios.