Weather forecast cares about plausible weather trajectories given incomplete knowledge of current weather status and imperfect forecasting models. Climate prediction cares about climate variability as revealed by a group of imperfect models, under various forcing scenarios. The distinction results from chaotic nature of geophysical fluid dynamics, putting a limit on weather predictability, endorsing climate prediction its in-deterministic nature, and leaving in between a battle field of predictability signal v.s. internal variability noise at subseasonal to seasonal scale. We break this long-standing distinction between weather forecast and climate prediction by quantifying the probabilistic distribution of climate state given observational and predictive constraints, using deep generative model. We demonstrate the unique advantage of this methodology for data assimilation, seamless forecast, and climate simulation.