HydroDiffusion: Diffusion‐Based Probabilistic Streamflow Forecasting With a State Space Backbone

Abstract

Recent advances have introduced diffusion models for probabilistic streamflow forecasting, demonstrating strong early flood‐warning skill. However, current implementations rely on Long Short‐Term Memory (LSTM) backbones and discrete‐time diffusion formulations. This leaves unresolved whether more advanced sequence‐modeling architectures and continuous‐time diffusion formulations can improve probabilistic streamflow forecasting. In this study, we developed HydroDiffusion, a diffusion‐based probabilistic forecasting framework integrating a decoder‐only state space model (SSM) backbone with a continuous‐time score‐based diffusion formulation. HydroDiffusion is evaluated across 531 watersheds in the contiguous United States (CONUS) in the CAMELS data set. We benchmark HydroDiffusion against two diffusion baselines with LSTM backbones, as well as the recently proposed Diffusion‐based Runoff Model (DRUM). Results show that HydroDiffusion achieves the strongest nowcast accuracy when driven by observed meteorological forcings. Moreover, HydroDiffusion delivers higher deterministic and probabilistic forecast skill than its LSTM‐based counterpart in operational forecasting. Attribution analysis further reveals that the SSM backbone excels in humid, densely vegetated, storage‐dominated watersheds with strong hydrologic memory, while its advantage becomes limited in arid regions and hydrologically complex systems such as karst and prairie pothole basins. These results establish HydroDiffusion as an effective generative modeling framework for medium‐range streamflow forecasting, providing both a new modeling benchmark and a foundation for future research on probabilistic hydrologic prediction at continental scales.