# Controllable Probabilistic Forecasting with Stochastic Decomposition Layers

arXiv: https://arxiv.org/abs/2512.18815 · HTML: https://mlsanity.com/paper/2512.18815/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 53 references that are in the map.
- First posted on arXiv 21 Dec 2025.

## Builds on (most cited first, 17 of 17)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [ClimaX: A foundation model for weather and climate](https://mlsanity.com/paper/2301.10343/) (2023)
- [FuXi: A cascade machine learning forecasting system for 15-day global weather forecast](https://mlsanity.com/paper/2306.12873/) (2023)
- [Neural General Circulation Models for Weather and Climate](https://mlsanity.com/paper/2311.07222/) (2023)
- [WeatherBench 2: A benchmark for the next generation of data-driven global weather models](https://mlsanity.com/paper/2308.15560/) (2023)
- [Forecasting Global Weather with Graph Neural Networks](https://mlsanity.com/paper/2202.07575/) (2022)
- [PreDiff: Precipitation Nowcasting with Latent Diffusion Models](https://mlsanity.com/paper/2307.10422/) (2023)
- [Skillful joint probabilistic weather forecasting from marginals](https://mlsanity.com/paper/2506.10772/) (2025)
- [FourCastNet 3: A geometric approach to probabilistic machine-learning weather forecasting at scale](https://mlsanity.com/paper/2507.12144/) (2025)
- [Machine Learning for Stochastic Parameterization: Generative Adversarial Networks in the Lorenz '96 Model](https://mlsanity.com/paper/1909.04711/) (2019)
- [Community Research Earth Digital Intelligence Twin (CREDIT)](https://mlsanity.com/paper/2411.07814/) (2024)
- [Mimicking non-ideal instrument behavior for hologram processing using neural style translation](https://mlsanity.com/paper/2301.02757/) (2023)

## Built on by (most cited first, 3 of 3)

- [U-Cast: A Surprisingly Simple and Efficient Frontier Probabilistic AI Weather Forecaster](https://mlsanity.com/paper/2604.09041/) (2026)
- [Conditional Tropical Cyclogenesis Rates via Rare-Event Sampling in a Neural Weather Emulator](https://mlsanity.com/paper/2606.30920/) (2026)
- [Rescene: band-limited stochastic forcing turns a frozen neural weather operator into a climate emulator](https://mlsanity.com/paper/2608.09971/) (2026)

## Abstract (arXiv)

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.