Generative Emulation on the Sphere: Bridging the Resolution Gap with Field-Space Diffusion

Probabilistic risk assessment requires large ensembles of high-resolution climate scenarios, yet generating such data is often computationally intractable. This study introduces a scalable generative framework designed to overcome the scarcity of high-fidelity climate data. We introduce the Field-Space Autoencoder, a geometric compression model that preserves the causal structure of atmospheric fields without forcing them onto regular lat-lon grids. Unlike standard deep learning approaches fixed to a single resolution, our method utilizes a multi-scale decomposition that stores a resolution-invariant latent representation. This flexibility unlocks a novel hybrid training strategy for generative diffusion: we combine the statistical robustness of multi-century, low-resolution simulations with the structural precision of limited high-resolution datasets. The resulting Compressed Field Diffusion model is capable of synthesizing atmospheric states that inherit the internal variability of the large ensemble and the spectral sharpness of the high-res ground truth. By bridging these data sources, we present a pathway to democratizing access to exascale-quality climate data through efficient, physically consistent emulation.