Turbulent flows, characterized by their chaotic and stochastic nature, have historically presented formidable challenges to predictive computational modeling. Traditional eddy-resolved numerical simulations often require vast computational resources, making them impractical or infeasible for numerous engineering applications. As an alternative, deep learning-based surrogate models have emerged, offering data-drive solutions. However, these are typically constructed within deterministic settings, leading to shortfall in capturing the innate chaotic and stochastic behaviors of turbulent dynamics. In this study, we introduce a novel generative framework grounded in probabilistic diffusion models for versatile generation of spatiotemporal turbulence under various conditions. Our method unifies both unconditional and conditional sampling strategies within a Bayesian framework, which can accommodate diverse conditioning scenarios, including those with a direct differentiable link between specified conditions and generated unsteady flow outcomes, as well as scenarios lacking such explicit correlations. A notable feature of our approach is the method proposed for long-span flow sequence generation, which is based on autoregressive gradient-based conditional sampling, eliminating the need for cumbersome retraining processes. We evaluate and showcase the versatile turbulence generation capability of our framework through a suite of numerical experiments, including: (1) the synthesis of Large Eddy Simulations (LES) simulated instantaneous flow sequences from unsteady Reynolds-Averaged Navier–Stokes (URANS) inputs; (2) holistic generation of inhomogeneous, anisotropic wall-bounded turbulence, whether from given initial conditions, prescribed turbulence statistics, or entirely from scratch; (3) super-resolved generation of high-speed turbulent boundary layer flows from low-resolution data across a range of input resolutions. Collectively, our numerical experiments highlight the merit and transformative potential of the proposed methods, making a significant advance in the field of turbulence generation.