HydroDiffusion: Diffusion-Based Probabilistic Streamflow Forecasting with a State Space Backbone

Recent advances have introduced diffusion models for probabilistic streamflow forecasting, demonstrating strong early flood-warning skill. However, current implementations rely on recurrent Long Short-Term Memory (LSTM) backbones and single-step training objectives, which limit their ability to capture long-range dependencies and produce coherent forecast trajectories across lead times. To address these limitations, we developed HydroDiffusion, a diffusion-based probabilistic forecasting framework with a decoder-only state space model backbone. The proposed framework jointly denoises full multi-day trajectories in a single pass, ensuring temporal coherence and mitigating error accumulation common in autoregressive prediction. HydroDiffusion is evaluated across 531 watersheds in the contiguous United States (CONUS) in the CAMELS dataset. 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 strong nowcast accuracy when driven by observed meteorological forcings, and maintains consistent performance across the full simulation horizon. Moreover, HydroDiffusion delivers stronger deterministic and probabilistic forecast skill than DRUM in operational forecasting. These results establish HydroDiffusion as a robust 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.