Many turbulence applications require instantaneous spatiotemporal realizations, not only mean statistics. Eddy-resolving simulations produce such information at high cost, while measurements are often sparse, noisy, or indirect. This Perspective argues that transport based generative models, including diffusion models and flow matching, should be viewed as reusable probabilistic priors for turbulence. Once trained, such priors can be queried conditionally without retraining, providing a unified framework for flow reconstruction, data assimilation, super-resolution, data restoration, and solver-constrained inference. We review this framework through three capabilities: forward generation, inverse conditioning, and scalable composition. Diffusion and flow-matching priors can synthesize temporally coherent turbulent realizations, condition samples on sparse or indirect information, and compose local patchwise priors for large domains beyond training. The goal is to generate an ensemble of plausible turbulent states consistent with data and physical constraints. We close by discussing validation criteria for generative turbulence priors, including distributional fidelity, non-memorization, data consistency, posterior calibration, physical admissibility, and large-domain coherence. Looking forward, such priors may serve as a statistical backbone for turbulence foundation models which are conditionable and uncertainty-aware, supporting predictive CFD, data assimilation, and decision-making workflows.