Schrödinger Bridge Data Assimilation with A Consistent Probabilistic View

Data assimilation (DA), which estimates the current atmospheric state by combining prior forecasts with sparse observations, is critical to the accuracy of modern weather prediction systems. The recently developed diffusion DA methods exhibit several superior aspects in comparison to the classical ones. Although DA targets a state distribution conditioned on both the background and observations, they learn a background-conditioned distribution during training and incorporate observations only during inference, separating observation conditioning from generative learning. To address this limitation, we propose Schrödinger Bridge Data Assimilation (SBDA), which integrates classical 3D-Var with diffusion Schrödinger bridges through an observation-enhanced reparameterization of DA conditioning, providing a consistent probabilistic treatment of observations across bridge learning and sampling. The resulting bridge generates analyses directly from observation-enhanced background states rather than Gaussian noise. We evaluate SBDA using background forecasts from a deep learning weather model, $1.5^{\circ }$ ERA5 reference fields, and simulated observations at 1% of the ERA5 grid points. SBDA achieves lower single-step assimilation errors than the evaluated baselines on most variables, with a mean relative reduction of 12.9% across all variables. More importantly, SBDA consistently improves downstream forecast across all variables, yielding a forecast time gain of up to 13.3 h relative to the strongest evaluated baseline. Furthermore, SBDA retains substantial assimilation gains at unseen observation locations without retraining.