Abstract
Bayesian data assimilation combines model forecasts with noisy observations, but sampling high-dimensional, non-Gaussian posteriors remains challenging. We introduce an observation-interpolant framework that turns pretrained stochastic interpolant, flow matching, and diffusion models into posterior samplers without retraining. Conditioning the interpolant path on observations yields a shared likelihood-score correction to the drift or velocity, unifying stochastic and deterministic posterior sampling. The resulting SDEs and ODEs sample the exact posterior when the intermediate likelihood score is known. For practical computation, we approximate this score using a closed-form Gaussian surrogate with a bias-corrected mean and covariance inflated by the model's source covariance. Jacobian-free and ensemble-shared approximations make the method tractable in high dimensions. We evaluate the framework on linear-Gaussian dynamics, stochastic two-dimensional Navier-Stokes, and urban airflow with up to $O(10^4)$ degrees of freedom.
Keywords
Publication details
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- Green open access
Cite this article
APA 7
Mücke, N. T., & Sanderse, B. (2026). A Unified Framework for Bayesian Data Assimilation with Generative Models and Observation Interpolants. https://omanscience.com/en/articles/a-unified-framework-for-bayesian-data-assimilation-with-generative-models-and-observation-interpolants
MLA 9
Mücke, Nikolaj T., and Benjamin Sanderse. "A Unified Framework for Bayesian Data Assimilation with Generative Models and Observation Interpolants." https://omanscience.com/en/articles/a-unified-framework-for-bayesian-data-assimilation-with-generative-models-and-observation-interpolants.
Chicago (author–date)
Mücke, Nikolaj T., and Benjamin Sanderse. 2026. "A Unified Framework for Bayesian Data Assimilation with Generative Models and Observation Interpolants." https://omanscience.com/en/articles/a-unified-framework-for-bayesian-data-assimilation-with-generative-models-and-observation-interpolants.
Harvard
Mücke, N. T. and Sanderse, B. (2026) 'A Unified Framework for Bayesian Data Assimilation with Generative Models and Observation Interpolants', Available at: https://omanscience.com/en/articles/a-unified-framework-for-bayesian-data-assimilation-with-generative-models-and-observation-interpolants.
Vancouver
Mücke NT, Sanderse B. A Unified Framework for Bayesian Data Assimilation with Generative Models and Observation Interpolants. https://omanscience.com/en/articles/a-unified-framework-for-bayesian-data-assimilation-with-generative-models-and-observation-interpolants
IEEE
N. T. Mücke, and B. Sanderse, "A Unified Framework for Bayesian Data Assimilation with Generative Models and Observation Interpolants," https://omanscience.com/en/articles/a-unified-framework-for-bayesian-data-assimilation-with-generative-models-and-observation-interpolants.