We train neural networks as denoising diffusion models for state generation in the chaotic Lorenz 1963 model and demonstrate that they learn an internal representation of its attractor. We make use of this learned representation and the pre-trained model in two downstream tasks: surrogate modelling and ensemble generation. For both tasks, the diffusion model can outperform other more common approaches. This paper also presents one of the very application of generative AI using diffusion models to ensemble data assimilation.

The paper, a contribution to the LEFE-MANU GenD2M and Schmidt Sciences SASIP projetcs, is entitled Representation learning with unconditional denoising diffusion models for dynamical systems, and is published in Nonlinear Processes in Geophysics.