From Continuous Fields to Discrete Tokens: Probabilistic Precipitation Nowcasting with Controlled-Path Diffusion

Precipitation nowcasting requires accurate forecasts of uncertain rainfall evolution at low computational cost. Diffusion models generate diverse forecasts, but their training and iterative sampling can limit practical use. We introduce Discrete Probabilistic Precipitation Nowcasting (DPPN), to our knowledge the first discrete diffusion framework for probabilistic precipitation nowcasting. DPPN encodes continuous radar fields into compact discrete tokens that form a learned vocabulary of precipitation patterns. By modeling their conditional evolution, DPPN offers a perspective on nowcasting as learning a weather language. DPPN connects continuous Gaussian relaxations with discrete token states to reduce training variance and improve computational efficiency. The framework supports two forecasting formulations: direct generation conditioned on historical observations and cascaded generation conditioned on a deterministic prediction. Both generate distributions over future tokens, with supervision on decoded precipitation fields guiding forecast reconstruction. Experiments on SEVIR demonstrate competitive forecasting performance relative to continuous diffusion and flow-matching baselines, with fewer trainable parameters and lower reported wall-clock costs under the evaluated implementations. The generated results highlight discrete diffusion as an efficient approach to probabilistic nowcasting and demonstrate its capacity for controllable generation through diffusion path design.