In recent years, machine learning has established itself as a powerful tool forhigh-resolution weather forecasting. While most current machine learning modelsfocus on deterministic forecasts, accurately capturing the uncertainty in thechaotic weather system calls for probabilistic modeling. We propose a probabilisticweather forecasting model called Graph-EFM, combining a flexible latent-variableformulation with the successful graph-based forecasting framework. The use of ahierarchical graph construction allows for efficient sampling of spatially coherentforecasts. Requiring only a single forward pass per time step, Graph-EFM allowsfor fast generation of arbitrarily large ensembles. We experiment with the modelon both global and limited area forecasting. Ensemble forecasts from Graph-EFMachieve equivalent or lower errors than comparable deterministic models, with theadded benefit of accurately capturing forecast uncertainty.