The importance of quantifying uncertainty in deep networks has become paramount for reliable real-world applications. In this paper, we propose a method to improve uncertainty estimation in medical Image-to-Image (I2I) translation. Our model integrates aleatoric uncertainty and employs Uncertainty-Aware Regularization (UAR) inspired by simple priors to refine uncertainty estimates and enhance reconstruction quality. We show that by leveraging simple priors on parameters, our approach captures more robust uncertainty maps, effectively refining them to indicate precisely where the network encounters difficulties, while being less affected by noise. Our experiments demonstrate that UAR not only improves translation performance, but also provides better uncertainty estimations, particularly in the presence of noise and artifacts. We validate our approach using two medical imaging datasets, showcasing its effectiveness in maintaining high confidence in familiar regions while accurately identifying areas of uncertainty in novel/ambiguous scenarios.