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This paper introduces a unified framework for Bayesian data assimilation that leverages pretrained generative models (stochastic interpolants, flow matching, diffusion models) as posterior samplers without requiring retraining. By conditioning the interpolant path on observations, the method derives a shared likelihood-score correction to the drift or velocity, unifying stochastic and deterministic posterior sampling. Practical computation is achieved by approximating the likelihood score with a bias-corrected Gaussian surrogate, enabling tractable high-dimensional inference.
Pretrained generative models can directly sample exact Bayesian posteriors for data assimilation by conditioning their interpolant paths on observations, bypassing costly retraining.
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.