Generative Spatiotemporal Modeling for Uncertainty Quantification in High-Dimensional Physical Systems

Forecasting high-dimensional chaotic systems, such as weather and turbulence, is fundamentally limited by uncertainty. Traditional deterministic models fail to capture this, collapsing to blurry, physically implausible mean-state predictions and offering no measure of confidence. We introduce Prism, a generative spatiotemporal framework that directly addresses this by learning the probability distribution of future states. Instead of regressing a single outcome, Prism, built on a conditional diffusion model, generates a diverse ensemble of high-fidelity, physically consistent future trajectories. This ensemble enables principled uncertainty quantification and improves the capture of low-probability, high-impact events. On standard benchmarks like WeatherBench and 2D turbulence, Prism significantly outperforms state-of-the-art baselines on probabilistic metrics such as the Continuous Ranked Probability Score (CRPS). Our work establishes generative modeling as a powerful paradigm for building trustworthy AI tools for scientific discovery.