Controllable Probabilistic Forecasting with Stochastic Decomposition Layers

AI weather prediction ensembles with latent noise injection and optimized with the continuous ranked probability score (CRPS) have produced both accurate and well-calibrated predictions with far less computational cost compared with diffusion-based methods. However, current CRPS ensemble approaches vary in their training strategies and noise injection mechanisms, with most injecting noise globally throughout the network via conditional normalization. This structure increases training expense and limits the physical interpretability of the stochastic perturbations. We introduce Stochastic Decomposition Layers (SDL) for converting deterministic machine learning weather models into probabilistic ensemble systems. Adapted from StyleGAN's hierarchical noise injection, SDL applies learned perturbations at three decoder scales through latent-driven modulation, per-pixel noise, and channel scaling. When applied to WXFormer via transfer learning, SDL requires less than 2\% of the computational cost needed to train the baseline model. Each ensemble member is generated from a compact latent tensor (5 MB), enabling perfect reproducibility and post-inference spread adjustment through latent rescaling. Evaluation on 2022 ERA5 reanalysis shows ensembles with spread-skill ratios approaching unity and rank histograms that progressively flatten toward uniformity through medium-range forecasts, achieving calibration competitive with operational IFS-ENS. Multi-scale experiments reveal hierarchical uncertainty: coarse layers modulate synoptic patterns while fine layers control mesoscale variability. The explicit latent parameterization provides interpretable uncertainty quantification for operational forecasting and climate applications.