[2603.21291] Closed-form conditional diffusion models for data assimilation

Statistics > Machine Learning arXiv:2603.21291 (stat) [Submitted on 22 Mar 2026] Title:Closed-form conditional diffusion models for data assimilation Authors:Brianna Binder, Assad Oberai View a PDF of the paper titled Closed-form conditional diffusion models for data assimilation, by Brianna Binder and Assad Oberai View PDF HTML (experimental) Abstract:We propose closed-form conditional diffusion models for data assimilation. Diffusion models use data to learn the score function (defined as the gradient of the log-probability density of a data distribution), allowing them to generate new samples from the data distribution by reversing a noise injection process. While it is common to train neural networks to approximate the score function, we leverage the analytical tractability of the score function to assimilate the states of a system with measurements. To enable the efficient evaluation of the score function, we use kernel density estimation to model the joint distribution of the states and their corresponding measurements. The proposed approach also inherits the capability of conditional diffusion models of operating in black-box settings, i.e., the proposed data assimilation approach can accommodate systems and measurement processes without their explicit knowledge. The ability to accommodate black-box systems combined with the superior capabilities of diffusion models in approximating complex, non-Gaussian probability distributions means that the proposed approach off...