Using Diffusion Models to do Data Assimilation

TL;DR

This paper explores the application of diffusion models in data assimilation for geophysical systems, analyzing different types of diffusion-based DA systems and their computational and statistical implications.

Contribution

It introduces a classification of diffusion-based data assimilation systems and examines their differences in targeting posterior distributions and computational costs.

Findings

Different diffusion DA systems target distinct posterior distributions.

Re-training is necessary for diffusion DA systems to match existing ensemble methods.

Diffusion DA systems have varying computational requirements depending on their design.

Abstract

The recent surge in machine learning (ML) methods for geophysical modeling has raised the question of how these methods might be applied to data assimilation (DA). We focus on diffusion modeling (a form of generative artificial intelligence) for systems that can perform the entire DA process, rather than on ML-based tools used within a conventional DA system. We identify at least three distinct types of diffusion-based DA systems and show that they differ in the posterior distribution they target for sampling. These posterior distributions correspond to different priors and/or likelihoods, which in turn result in unique training datasets, computational requirements, and state estimate qualities. Our analysis further shows that a diffusion DA system designed to target the same posterior distribution as current ensemble DA algorithms requires re-training at each DA cycle, which is computationally costly. We discuss the implications of these findings for the use of diffusion modeling in DA.