Most operational climate services providers base their seasonal predictions on initialised general circulation models (GCMs) or statistical techniques that fit past observations. GCMs require substantial computational resources, which limits their capacity. In contrast, statistical methods often lack robustness due to short historical records. Recent works propose machine learning methods trained on climate model output, leveraging larger sample sizes and simulated scenarios. Yet, many of these studies focus on prediction tasks that might be restricted in spatial extent or temporal coverage, opening a gap with existing operational predictions. Thus, the present study evaluates the effectiveness of a methodology that combines variational inference with transformer models to predict fields of seasonal anomalies. The predictions cover all four seasons and are initialised one month before the start of each season. The model was trained on climate model output from CMIP6 and tested using ERA5 reanalysis data. We analyse the method's performance in predicting interannual anomalies beyond the climate change-induced trend. We also test the proposed methodology in a regional context with a use case focused on Europe. While climate change trends dominate the skill of temperature predictions, the method presents additional skill over the climatological forecast in regions influenced by known teleconnections. We reach similar conclusions based on the validation of precipitation predictions. Despite underperforming SEAS5 in most tropics, our model offers added value in numerous extratropical inland regions. This work demonstrates the effectiveness of training generative models on climate model output for seasonal predictions, providing skilful predictions beyond the induced climate change trend at time scales and lead times relevant for user applications.