Uncertainty Quantification in Generative Climate Downscaling: A Multi-Ensemble DDPM Analysis

Deterministic deep learning models used for climate downscaling often exhibit spectral collapse, resulting in overly smoothed fields that underestimate extreme events. Although Generative Adversarial Networks (GANs) can preserve high-frequency details, their training instability limits the reliability of ensemble generation. Denoising Diffusion Probabilistic Models (DDPMs) offer a solution to both of these problems. They sample from learned probability distributions through iterative denoising, which introduces inherent randomness. This allows each inference to produce statistically different but physically plausible results, a feature that is essential for quantifying uncertainty in climate projections. This study presents the first systematic analysis of ensemble convergence for DDPM-based climate downscaling at a 10× spatial resolution (1.0° → 0.1°). We evaluated configurations with ensemble sizes ranging from 2 to 50 members, focusing on 30 extreme temperature events. Using the multi-modal sampling capabilities of DDPMs, achieved through different random initializations in the reverse diffusion process, we assessed the trade-offs between accuracy, uncertainty, and computational cost. This was done using a set of metrics: RMSE, MAE, Pearson R, SSIM, and PSNR. The research results demonstrate significant convergence trends: (1) ensemble mean predictions exhibit rapid saturation, with 5-member configurations attaining 96–98% of peak performance (RMSE: 0.459°C compared to 0.453°C for 25 members); (2) spatial uncertainty estimates (0.165–0.170°C) stabilize at 5–10 members, with only minor enhancements of less than 1% beyond this point; (3) computational costs increase substantially, a 50-member ensembles necessitate 35 hours, whereas 5-member ensembles require only 4 hours, indicating an 89% reduction in cost with minimal compromise in accuracy. The optimal range of 5–10 members provides strong uncertainty constraints and enables operational scalability in continental-scale applications. In contrast to deterministic models that provide only point estimates or GANs prone to mode collapse, DDPMs' generative sampling inherently quantifies prediction confidence via ensemble spread, thereby encompassing both epistemic model uncertainty and aleatoric variability. This research provides actionable guidance for uncertainty-aware climate downscaling, demonstrating that small DDPM ensembles effectively produce probabilistic projections, which are crucial for evaluating climate risk.