Pairwise Consistency Models for Bayesian Transport and Variational Data Assimilation

Bayesian inference in high-dimensional dynamical systems is traditionally approached through either score-based diffusion models or variational data assimilation. Although developed independently, both rely on the numerical integration of continuous Bayesian transport dynamics, making inference computationally expensive. We introduce a unified pairwise consistency framework that learns finite-time Bayesian transport operators between arbitrary solver times instead of infinitesimal transport fields. By enforcing pairwise consistency, the proposed approach preserves the semigroup structure of the underlying flow while avoiding explicit integration of the transport dynamics. This perspective naturally generalizes consistency models beyond diffusion processes and extends to variational inference without requiring an explicit forward diffusion model. The resulting framework encompasses supervised diffusion learning, self-consistent variational optimization, and hybrid diffusion–physical transport within a common mathematical formulation. Experiments on synthetic and geophysical inverse problems demonstrate efficient few-step reconstruction, sequential forecasting, and uncertainty-aware posterior sampling, showing that finite-time transport learning provides an effective alternative to conventional score-based integration.