Turbulent flows in natural and engineered environments exhibit strongly unsteady, chaotic and multiscale dynamics. In wind farms, this fundamentally limits the predictive modeling required for real-time turbine control strategies. This challenge is compounded by the various uncertainties in the inputs e.g. wind speed and direction, terrain and atmospheric boundary layer stability. Data assimilation can reduce uncertainty by combining observations with models. Traditional approaches rely on computationally expensive deterministic simulations and subsequent correction step, limiting their scalability and real-time applicability. Generative models offer a new promising avenue. Here we show on turbulent plane Couette flow as a canonical wall-bounded flow that a stochastic generative model efficiently generate and assimilate turbulent flow fields under sparse observational constraints. By combining a variational autoencoder for dimensionality reduction with a transformer-based diffusion process, the model generates four-dimensional spatiotemporal flow trajectories. Sparse measurements are incorporated through Bayesian posterior sampling, enabling conditional generation without retraining. Our results demonstrate that generate flow fields reproduce key statistical quantities of the reference DNS data up to fourth order moments using a compact latent representation with fewer than 40 degrees of freedom. We also demonstrate that the model can perform two distinct data assimilation tasks without the need for retraining. These results demonstrate that generative diffusion models can provide scalable probabilistic priors for turbulent flows. Furthermore, it establishes a foundation for real-time reconstruction of wind farm flow fields from sparse operational data. We anticipate that this framework can be extended to operating conditions beyond those represented in the training data.