Deep learning algorithms have been widely used in microscopic image translation. The corresponding data-driven models can be trained by supervised or unsupervised learning depending on the availability of paired data. However, general cases are where the data are only roughly paired such that supervised learning could be invalid due to data unalignment, and unsupervised learning would be less ideal as the roughly paired information is not utilized. In this work, we propose a unified framework (U-Frame) that unifies supervised and unsupervised learning by introducing a tolerance size that can be adjusted automatically according to the degree of data misalignment. Together with the implementation of a global sampling rule, we demonstrate that U-Frame consistently outperforms both supervised and unsupervised learning in all levels of data misalignments (even for perfectly aligned image pairs) in a myriad of image translation applications, including pseudo optical sectioning, virtual histological staining (with clinical evaluations for cancer diagnosis), improvement of signal-to-noise ratio or resolution, and prediction of fluorescent labels, potentially serving as new standard for image translation.