Can Wavelet-Aware Diffusion Improved Streamflow Forecasting Outcomes?

Long-term streamflow forecasts must represent uncertainty across daily and sea- sonal scales. We compare where wavelet knowledge helps a conditional diffu- sion forecaster most: injected into the training objective as Morlet wavelet-power matching, or into the architecture as fixed Morlet feature channels in the histori- cal encoder. The model generates 365-day forecast ensembles from 180 days of historical streamflow and meteorology. Trained across 901 unregulated Canadian gauges and evaluated on 50 basins over five forecast years against a full-record climatological ensemble, wavelet-aware training restores the high-frequency vari- ability that pointwise objectives smooth away. Both wavelet methods significantly reduce annual usable-flow error relative to climatology (10% via loss, 7% via encoder). Wavelet loss results in larger operational and volumetric gains, while wavelet encoding captures much of the energy benefit through conditioning alone.