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

TL;DR

The paper tackles the common problem of blurry predictions in earth-system nowcasting by applying score-based diffusion models to GOES-16 infrared imagery. It compares three diffusion approaches—Diff, CorrDiff, and a latent diffusion model (LDM)—and demonstrates that CorrDiff offers the best balance of sharpness, accuracy, and uncertainty quantification, outperforming a traditional U-Net and persistence in 3-hour forecasts. A case study and large-scale evaluation show diffusion models can generate, advect, and even initiate convection, while enabling ensemble generation for probabilistic forecasting. The work provides practical guidance, discusses trade-offs between performance and compute, and contributes an accessible, open framework for adopting diffusion methods in Earth and Environmental Science tasks.

Abstract

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.

Figures (16)

• Figure 1: Graphic illustration of what the distribution of training data looks like, both in its 2d shape as images (left) and a 1d representation for conceptualization (right, the histogram representing the pixel-value distribution).
• Figure 2: Schematic describing main task for diffusion models: seeking a way to sample from an unknown distribution, ${\mathcal{X}}$, by sampling from a known distribution, such as a Gaussian distribution, $\mathcal{N}(\mu,\sigma)$.
• Figure 3: A visual diagram illustrating conceptually the forward and backward process for a diffusion model. The left column shows the simplified 1-d representations of distributions. The center column shows single image examples. The right column shows all 1-d representations of the data, which is known as $x-\sigma$ diagram in the computer science literature. Note that we switched the axes of the $x-\sigma$ diagram - in comparison to the literature - to emphasize the relationship to the histograms in the left column. Namely, each histogram on the left represents one $\sigma$ value and corresponds to one horizontal line in the $x-\sigma$ diagram on the right.
• Figure 4: $x-\sigma$ diagram illustrating one iteration of the backward process of a diffusion model, namely the transition from one image, A, to the next image, B, that is closer to the distribution of $\mathcal{X}$, using the gradient term, $\nabla_{\bm{x}} \log p(\bm{x}, \sigma)$.
• Figure 5: A schematic describing one batch of data through the training process of an unconditional diffusion model.