  This work presents an autoregressive generative diffusion model (DiffObs) to
predict the global evolution of daily precipitation, trained on a satellite
observational product, and assessed with domain-specific diagnostics. The model
is trained to probabilistically forecast day-ahead precipitation. Nonetheless,
it is stable for multi-month rollouts, which reveal a qualitatively realistic
superposition of convectively coupled wave modes in the tropics. Cross-spectral
analysis confirms successful generation of low frequency variations associated
with the Madden--Julian oscillation, which regulates most subseasonal to
seasonal predictability in the observed atmosphere, and convectively coupled
moist Kelvin waves with approximately correct dispersion relationships. Despite
secondary issues and biases, the results affirm the potential for a next
generation of global diffusion models trained on increasingly sparse, and
increasingly direct and differentiated observations of the world, for practical
applications in subseasonal and climate prediction.
