Estimating the unresolved geophysical processes from resolved geophysical fluid dynamics is the key for improving numerical weather-climate predictions. While data-driven parameterization for unresolved geophysical processes shows potential, most practices fail to capture the diversity of unresolved geophysical processes that agree with resolved geophysical fluid state. This pitfall undermines the likelihood or severity of simulated weather extremes, and erodes the fidelity of climate projections. We propose the criteria of READS (Realism, Efficiency, Adaptability, Diversity, Sharpness) for generative models to yield reasonable stochastic parameterization. We introduce probabilistic diffusion model, a non-equilibrium thermodynamics inspired deep generative modeling approach, to better meet these criteria. Using a case example of numerical precipitation estimation, we demonstrate the advantage of the proposed methodology in quickly delivering diverse and faithful estimates for the target unresolved process, as compared to other popular data-driven deterministic and stochastic methods (UNet, variational autoencoder, generative adversarial net), as well as dynamical downscaling method (WRF). We conclude that generative models, in particular, probabilistic diffusion model, can significantly enhance the representation of unresolved geophysical processes in numerical weather-climate predictions.