Deep learning for meteorological downscaling: from deterministic super-resolution to probabilistic and multi-variable models

High-resolution meteorological data is essential for understanding and predicting atmospheric processes, yet their production remains limited by the high computational cost of numerical downscaling models. In recent years, deep learning has emerged as a viable and highly efficient alternative, capable of producing high-quality, high-resolution fields at a fraction of the computational expense. This thesis explores the landscape of deep learning approaches for climate downscaling, analyzing their limitations and introducing new architectural designs and methodologies that enhance accuracy, represent uncertainty, and exploit inter-variable relationships. Alongside establishing a general methodological framework that maps existing neural downscaling approaches, the thesis comprises three original studies that collectively advance the state of data-driven downscaling. The first applies diffusion models to the super-resolution of near-surface wind speed from ERA5 to CERRA, benchmarking a range of architectures and introducing an ensemble diffusion formulation that achieves state-of-the-art accuracy while reproducing fine-scale variability. The second develops a theoretical link between the number of reverse diffusion steps and model variance, enabling calibrated uncertainty control and efficient ensemble generation. This framework is validated against existing ensemble reanalyses and extended to regions lacking ensemble information, positioning diffusion models as practical tools for uncertainty-aware meteorological modeling. The third study introduces a multi-variable, multi-task Vision Transformer that jointly downscales six meteorological variables, demonstrating that shared spatial representations improve both accuracy and efficiency compared to single-variable approaches. Together, these contributions provide new methodological insights into the use of generative and transformer-based architectures for climate and weather applications. They highlight how deep learning can evolve from merely reproducing existing models to discovering new representations of atmospheric variability and coherence.