Data assimilation (DA) addresses the problem of sequentially estimating the state of a dynamical system from noisy and incomplete observations. In this work, we employ a diffusion model as a world model to simulate and predict the system's dynamics. Recently, score-based diffusion models have learned global diffusion priors that effectively model (stochastic) dynamics, revealing strong potential for data assimilation. In this paper, we investigate how information from noisy observations can be incorporated to enable continuous correction and refinement of the predicted system state when using a diffusion prior. Motivated by particle filtering methods, we represent the posterior distribution using a set of particles. After receiving noisy observations, the diffusion model is guided using the observation likelihood to steer the generation process toward observation-consistent states. Nevertheless, such guidance does not guarantee sampling from the true posterior. We therefore employ a Sequential Monte Carlo approach over the diffusion trajectory, viewed as a path measure, to reweight and resample particles, thereby correcting the generation process and ensuring convergence toward the desired posterior distribution. This leads to an unbiased particle filtering method that rigorously fuses observational data with diffusion model simulations.

翻译：数据同化（DA）旨在解决从含噪且不完整的观测中序贯估计动力系统状态的问题。本研究采用扩散模型作为世界模型来模拟和预测系统动态。近期，基于分数的扩散模型通过学习全局扩散先验能够有效建模（随机）动态，展现出在数据同化领域的巨大潜力。本文探究了在采用扩散先验时，如何通过融合含噪观测信息实现对预测系统状态的连续校正与精化。受粒子滤波方法启发，我们采用粒子集合表示后验分布。在接收含噪观测后，通过观测似然引导扩散模型，使生成过程偏向于与观测一致的状态。然而，这种引导无法保证从真实后验分布中采样。为此，我们沿扩散轨迹（视为路径测度）采用序贯蒙特卡洛方法对粒子进行加权与重采样，从而纠正生成过程并确保收敛至目标后验分布。该方法构建了一种无偏粒子滤波框架，能够严格地将观测数据与扩散模型模拟相融合。