We propose a novel method for reconstruction of high-resolution Sea Surface Height (SSH) fields from sparse along-track satellite altimetry. We explore the usage of an observation-driven deep-learning method for inpainting, with a focus on diffusion-based generative models for spatial reconstruction and data assimilation. The study includes data preparation from reanalyses and satellite observations, the definition of evaluation metrics relevant to oceanography, and comparison with baselines. We discuss model design choices, uncertainty characterization through stochastic sampling, and limitations in real-world deployment. Effectively, in this work, we develop and validate an observation-driven prior, allowing us to sample from the ground-truth distribution of SSH. By not relying on simulation results for training, we propose a step towards observationdriven Deep-Learning analysis of SSH and its uncertainties at small scales