Recently, deep learning (DL) approaches have become the main research frontier for biological image reconstruction and enhancement problems thanks to their high performance and ultrafast inference times. However, due to the difficulty of obtaining matched reference data for supervised learning, there has been increasing interest in unsupervised learning approaches that do not need paired reference data. In particular, self-supervised learning and generative models have been successfully used for various biological imaging applications. In this article, we provide an overview of these approaches from a coherent perspective in the context of classical inverse problems and discuss their applications to biological imaging, including electron, fluorescence, deconvolution microscopy, optical diffraction tomography (ODT), and functional neuroimaging.