DAISI: Data Assimilation with Inverse Sampling using Stochastic Interpolants

Data assimilation (DA) is a cornerstone of scientific and engineering applications, combining model forecasts with sparse and noisy observations to estimate latent system states. Classical high-dimensional DA methods, such as the ensemble Kalman filter, rely on Gaussian approximations that are violated for complex dynamics or observation operators. To address this limitation, we introduce DAISI, a scalable filtering algorithm built on flow-based generative models that enables flexible probabilistic inference using data-driven priors. The core idea is to use a stationary, pre-trained generative prior that first incorporates forecast information through a novel inverse-sampling step, before assimilating observations via guidance-based conditional sampling. This allows us to leverage any forecasting model as part of the DA pipeline without having to retrain or fine-tune the generative prior at each assimilation step. Experiments on challenging nonlinear systems show that DAISI achieves accurate filtering results in regimes with sparse, noisy, and nonlinear observations where traditional methods struggle. The code for DAISI is available at https://github.com/Erik-Wikingsson/DAISI.

Weather forecasting is essential for many parts of society, from early warning systems and agriculture to renewable energy management. To predict tomorrow’s weather accurately, we first need a good estimate of today’s atmospheric state. While we have many observations from satellites and sensors around the world, they can be noisy, biased, or completely missing in remote regions. Data assimilation (DA) addresses this by combining observations with the previous forecast to produce the best possible estimate of the current state. Although DA is used in operational weather prediction systems every day, many of these methods still rely on simplifying assumptions and careful manual tuning. We propose DAISI, a new data assimilation method that uses generative modelling to learn realistic atmospheric states and then integrates forecasts and new observations in a principled way. This leads to more accurate state estimates, especially in challenging situations with sparse or complex observations.