New UQ Method Integrates Joint Aleatoric and Epistemic Uncertainties

This research addresses a critical challenge in deep learning: enhancing the reliability of predictions, especially in applications with high-dimensional output spaces like medical image segmentation or restoration. The paper focuses on the dual nature of uncertainty – aleatoric, which stems from inherent data noise, and epistemic, which reflects the model's confidence or knowledge gaps. Traditionally, these are often treated separately, limiting the transparency and robustness of predictions. The proposed novel approach explicitly combines both types of uncertainties into a unified second-order distribution. To manage the computational burden of high-dimensional outputs, it approximates the resulting joint uncertainty using a low-rank plus diagonal covariance structure, effectively capturing essential output correlations. This method supports robust downstream analyses such as sampling and log-likelihood evaluation and includes stabilization strategies for efficient training and inference, demonstrating superior UQ performance in tasks like image inpainting, colorization, optical flow, and depth estimation.