Consider two illustrative rivers. One flows steadily at 40 cubic metres a second. The other flows at 20 for eighteen hours, then 100 for six hours. Both average 40 over the day; the second peaks 2.5 times higher. A daily number conceals that difference.
Wencong Yang and colleagues tested h-Diffusion retrospectively in 516 US catchments. Their July paper in Water Resources Research combines hourly prediction with the assimilation of recent gauge observations.[1]
Borrowing an image-editing idea
In image inpainting, a model fills a missing region while retaining information from the visible picture. RePaint, introduced at CVPR in 2022, does this with a diffusion model: successive denoising steps generate missing content while the known region supplies a continuing constraint. The procedure changes how an existing model generates an answer without retraining its underlying network.[2]
The river application transfers that arrangement into time. The released software generates 72 hourly values using weather inputs, daily context, catchment characteristics and daily flow information. Its generation code can insert recent measured values through inpainting.[3]
The tests assessed the final 24 hours, using simulated daily flows. The assimilation run supplied gauge readings with a five-hour lag.[1]
Picture a curve rising from left to right. If a gauge establishes that its early section should be higher, simply replacing that section could leave an abrupt join. Repeated generation around the known values gives the model a way to reconcile the rest of the curve with the observation. This is the logic of the method, illustrated rather than a separate experiment.[2]
The code also produces multiple realisations from a trained checkpoint. That allows a family of possible hourly curves rather than requiring one deterministic line. The usefulness of that spread still depends on how well it represents observed outcomes; producing several answers is only the means of representing uncertainty.[3]
The gauge information made the larger difference
With a single hourly weather-input product, median Nash–Sutcliffe efficiency was 0.763 for an established LSTM baseline, 0.780 for h-Diffusion and 0.832 after gauge assimilation. The score is 1 for a perfect fit and 0 for predicting the observed mean; it is not percentage accuracy.[1]
The diffusion model without recent gauge readings produced a modest gain over that hourly baseline. Adding measured river behaviour produced the larger one. The five-hour lag describes how recent the available observations were, rather than a demonstrated five-hour extension of public warning time.
With several weather products, the NSE results of the three models without assimilation were statistically indistinguishable. Benefits also weakened for the rarest high flows. The tests used historical meteorological products, leaving operational performance with forecast weather to be demonstrated.[1]
A measured river flow is therefore valuable twice: as the quantity a forecast is judged against, and as information that can alter the next generated curve. h-Diffusion provides a practical mechanism for the second use. The scientific result is the improvement achieved when those observations are admitted into the calculation.
Sources & further reading
- Diffusion-Based Probabilistic Modeling for Hourly Streamflow Prediction and Assimilation — Yang and colleagues Water Resources Research · 21 Jul 2026 · Accessed 19 Oct 2026
- RePaint: Inpainting Using Denoising Diffusion Probabilistic Models — Lugmayr and colleagues Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition 2022 · Accessed 19 Oct 2026
- Code for Diffusion-Based Probabilistic Modeling for Hourly Streamflow Prediction and Assimilation Wencong Yang / Zenodo · 17 Jul 2026 · Accessed 19 Oct 2026