CEDDAR v1.0.2: Bridging physics and generative modelling for regional precipitation with controllable diffusion-based downscaling

Abstract. Understanding local impacts of extreme weather, from e.g. precipitation or temperature, requires high-resolution downscaling of those atmospheric variables. Deterministic and classical statistical methods fail to adequately represent variability and extremes, motivating the use of probabilistic generative methods. Recent advances in generative deep learning show promise for spatial realism and ensemble generation, but their physical fidelity and limitations remain insufficiently understood.

We present CEDDAR v1.0.2 (Controllable Ensemble Diffusion Downscaling for Atmospheric Rainfall), a diffusion-based generative model for daily precipitation downscaling, conditioned on large-scale (∼30 × 30 km) ERA5 precipitation fields, to produce kilometre-scale (2.5 × 2.5 km) precipitation over Denmark, using the DANish ReAnalysis product (DANRA) as reference. The modelling framework is based on an Elucidated Diffusion Model (EDM) backbone and incorporates soft physics-guidance through seasonal (Day-of-Year) and geographic conditioning with a specific land-focused design.We further introduce regularisation terms through a Signed-Distance Function weighted loss, and an auxiliary RainGate head for shaping wet-dry occurrence statistics and improving ensemble calibration.

By design, the model is probabilistic and capable of producing ensembles. We further introduce an inference-time control parameter, σ^*, that allows for interpretable adjustment of stochastic scale sensitivity without retraining. For model-behaviour assessment, we introduce a multi-perspective evaluation protocol with emphasis on trade-offs across probabilistic, spatial, climatological, and scale-dependent diagnostics rather than single-metric optimisation.

Our results show strong spatial and spectral realism with generally well-calibrated ensembles, but also demonstrate that visually realistic fine-scale structure does not guarantee climatological fidelity. We also find that explicitly introducing σ^* reveals systematic, though non-linear, trade-offs between large-scale coherence, fine-scale variability, and ensemble spread. This highlights the potential and the limitations of controllable diffusion-based downscaling.

In conclusion, this work presents a diffusion-based downscaling framework and evaluation suite that works as a diagnostic testbed for understanding how generative models behave in physically constrained settings, and offers guidance on their appropriate use and common failure modes relevant to future operational solutions and climate-impact applications.