How to use score-based diffusion in earth system science: A satellite nowcasting example

Machine learning (ML) is used for many earth science applications; however, traditional ML methods trained with squared errors often create blurry forecasts. Diffusion models are an emerging generative ML technique with the ability to produce sharper, more realistic images by learning the underlying data distribution. Diffusion models are becoming more prevalent, yet adapting them for earth science applications can be challenging because most articles focus on theoretical aspects of the approach, rather than making the method widely accessible. This work illustrates score-based diffusion models with a well-known problem in atmospheric science: cloud nowcasting (zero-to-three-hour forecast). After discussing the background and intuition of score-based diffusion models using examples from geostationary satellite infrared imagery, we experiment with three types of diffusion models: a standard score-based diffusion model (Diff); a residual correction diffusion model (CorrDiff); and a latent diffusion model (LDM). Our results show that the diffusion models not only advect existing clouds, but also generate and decay clouds, including convective initiation. A case study qualitatively shows the preservation of high-resolution features longer into the forecast than a conventional U-Net. The best of the three diffusion models tested was the CorrDiff approach, outperforming all other diffusion models, the conventional U-Net, and persistence. The diffusion models also enable out-of-the-box ensemble generation with skillful calibration. By explaining and exploring diffusion models for a common problem and ending with lessons learned from adapting diffusion models for our task, this work provides a starting point for the community to utilize diffusion models for a variety of earth science applications.

💡 Research Summary

This paper introduces score‑based diffusion models as a practical tool for satellite nowcasting, specifically forecasting geostationary infrared (IR) brightness temperatures 0–3 hours ahead. The authors begin by highlighting the limitations of conventional deep‑learning approaches trained with mean‑squared‑error loss, which tend to produce blurry predictions, and note the training instability and poor uncertainty quantification of GANs. They then present score‑based diffusion (SBD) as an emerging generative technique that learns the full data distribution and can generate sharp, physically plausible images.

The methodological core follows the EDM (Elucidating the Design space of diffusion‑based Generative Models) framework, which generalizes the earlier DDPM approach but offers better computational efficiency—crucial for operational forecasting. Three model variants are implemented and compared: (1) a plain diffusion model (Diff), which directly denoises noisy images in pixel space; (2) a residual‑correction diffusion model (CorrDiff), which takes a conventional U‑Net forecast as input and learns to correct its residual errors; and (3) a latent diffusion model (LDM), which first compresses images with a pretrained autoencoder and performs diffusion in the lower‑dimensional latent space, thereby reducing memory and compute demands.

The dataset consists of GOES‑16/17 IR channel (10.3 µm) imagery sampled every 10 minutes. Standard preprocessing steps—cloud masking, spatial‑temporal normalization, and train‑test split—are applied. All models share the same noise schedule, learning‑rate warm‑up, and are trained on four NVIDIA A100 GPUs for roughly 200 k steps.

Quantitative results show that CorrDiff consistently outperforms Diff, the baseline U‑Net, and a persistence forecast across PSNR, SSIM, and structural similarity metrics, especially at the 2–3 hour lead times where it preserves high‑resolution cloud features and even captures convective initiation. Diff captures bulk motion but loses fine detail, while LDM achieves the lowest computational cost but sacrifices some texture fidelity.

A notable advantage of diffusion models is their intrinsic stochastic sampling, which the authors exploit to generate 30‑member ensembles without extra training. Calibration diagnostics (Brier score, reliability diagrams) demonstrate that the ensemble forecasts are well‑calibrated, addressing a common shortcoming of GAN‑based ensembles that tend to be under‑dispersive.

The discussion outlines practical trade‑offs: CorrDiff offers the best accuracy but highest resource demand; LDM is suitable for real‑time deployment with limited hardware; Diff serves as a middle‑ground baseline. The authors also provide a “recipe” of implementation tips—noise‑level scheduling, residual conditioning, data augmentation, and evaluation protocols—to lower the barrier for Earth‑system scientists.

In conclusion, the study validates that score‑based diffusion models can deliver sharper, more physically realistic nowcasts and reliable probabilistic ensembles for satellite imagery, paving the way for broader adoption in climate, hydrology, and other Earth system applications.