Abstract
<title>Abstract</title> <p>Kilometre-scale daily precipitation forecasts at Sub-seasonal to Seasonal (S2S) lead times are critical for climate-sensitive sectors, but General Circulation Model (GCM) outputs are coarse and biased. Their ensemble nature also undermines traditional downscaling methods such as Quantile Mapping, which assume predefined relationships. Generative Adversarial Networks (GANs) can generate realistic precipitation fields but are unstable to train, while diffusion models struggle with mismatched coarse-to-fine training pairs and frequent zero-precipitation values. This study introduces the Conditional Diffusion Downscaling Model (CDDM), which frames S2S downscaling as conditional image translation from coarse GCM forecasts to fine-resolution observed precipitation fields. Drawing on the Brownian bridge process, CDDM modifies standard forward diffusion by terminating at a hybrid state that blends the coarse forecast with controlled Gaussian noise, rather than pure noise. The reverse process, conditioned on the raw GCM forecast, then learns a stochastic mapping to fine-scale precipitation fields. A composite loss function combining Mean Absolute Error (MAE) and relative Bias (rBias) further improves forecast accuracy.CDDM is evaluated by downscaling nine-member ACCESS-S2 ensemble forecasts from 60 km to 5 km resolution over eastern Australia. Averaged over three evaluation years and 42-day forecast horizons, CDDM consistently outperforms QM, a climatology benchmark, and a state-of-the-art GAN across probabilistic and deterministic metrics, including the continuous ranked probability score (CRPS), MAE, and rBias. It achieves improvements of at least 8.29\% in CRPS and 9.01\% in MAE, and remains robust across La Niña, neutral, and El Niño conditions.</p>