  Data assimilation has become a crucial technique aiming to combine physical
models with observational data to estimate state variables. Traditional
assimilation algorithms often face challenges of high nonlinearity brought by
both the physical and observational models. In this work, we propose a novel
data-driven assimilation algorithm based on generative models to address such
concerns. Our State-Observation Augmented Diffusion (SOAD) model is designed to
handle nonlinear physical and observational models more effectively. The
marginal posterior associated with SOAD has been derived and then proved to
match the real posterior under mild assumptions, which shows theoretical
superiority over previous score-based assimilation works. Experimental results
also indicate that our SOAD model may offer improved accuracy over existing
data-driven methods.
