Data assimilation (DA) is essential for estimating the state of complex dynamical systems by combining models with noisy observations. However, efficient posterior sampling in high-dimensional, non-linear systems remains a significant computational bottleneck. Traditional Bayesian methods like Particle Filters are often computationally prohibitive, while efficient ensemble-based approaches typically rely on restrictive Gaussian assumptions [1]. In this work, we present a novel framework for posterior sampling in DA using Stochastic Interpolants (SIs), a class of generative models that transform probability distributions via stochastic differential equations (SDEs) [2,3,4]. We derive a posterior SDE that incorporates observational data through a drift correction term, enabling posterior sampling without model retraining. To ensure computational tractability, we introduce a method based on observation interpolation to evaluate likelihood scores efficiently, avoiding expensive integration over intermediate states. We demonstrate the efficacy of our method on test cases including 2D stochastic incompressible Navier-Stokes equations and a 2D slice of a 3D turbulent urban airflow simulation and compare with alternative approaches based on generative models. [1] Evensen, G, Vossepoel, F. C. and Van Leeuwen, P. J. Data assimilation fundamentals: A unified formulation of the state and parameter estimation problem. Springer Nature, 2022. [2] Albergo, M. S., Boffi, N. M., and Vanden-Eijnden, E., Stochastic interpolants: A unifying framework for flows and diffusions. arXiv preprint arXiv:2303.08797, 2023 [3] Chen, Y., Goldstein, M., Hua, M., Albergo, M. S., Boffi, N. M., and Vanden-Eijnden, E., Probabilistic forecasting with stochastic interpolants and f¨ollmer processes. arXiv preprint arXiv:2403.13724, 2024 [4] M¨ucke, N. T. and Sanderse, B. ”Physics-aware generative models for turbulent fluid flows through energy-consistent stochastic interpolants.” arXiv preprint arXiv:2504.05852, 2025.