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.

翻译：数据同化已成为一项关键技术，旨在将物理模型与观测数据相结合以估计状态变量。传统的同化算法常常面临物理模型和观测模型带来的高度非线性挑战。在本工作中，我们提出了一种基于生成模型的新型数据驱动同化算法以应对这些问题。我们设计的状态观测增强扩散（SOAD）模型能更有效地处理非线性物理模型与观测模型。我们推导了SOAD相关的边缘后验分布，并在温和假设下证明其与真实后验分布一致，这显示了其在理论上优于先前基于分数的同化工作。实验结果也表明，我们的SOAD模型相比现有数据驱动方法可能提供更高的精度。