Stabilizing Probabilistic Forecasts via Stochastic Interpolation Cascades

We study whether generative forecasters sample the correct distribution of future states given coarse observations of a physical system. We build a benchmark pairing observed coarse-grained states with many future states generated by varying the unobserved variables, which enables direct evaluation of conditional distributions. The benchmark reveals that commonly used diffusion models and stochastic interpolants trained directly over long forecast horizons can generate samples with plausible spatial statistics but substantially mismatched conditional distribution. We then propose and analyze a stylized mathematical model of dynamics and prove the existence of a regime where learning and composing shorter transitions outperforms learning the full transition directly. Shorter transitions reduce approximation error, while repeated conditioning can discard hidden information, leading to an optimal intermediate number of stages. This analysis motivates Cascaded SI, which implements staged forecasting with stochastic interpolants. Experiments across several physical systems show substantial improvements in conditional sampling, with gains persisting when the number of supervised transitions is held fixed.