Phase unwrapping (PU) is a technique to reconstruct original phase images from their noisy wrapped counterparts, finding many applications in scientific imaging. Although supervised learning has shown promise in PU, its utility is limited in ground-truth (GT) scarce scenarios. This paper presents an unsupervised learning approach that eliminates the need for GTs during end-to-end training. Our approach leverages the insight that both the gradients and wrapped gradients of wrapped phases serve as noisy labels for GT phase gradients, along with sparse outliers induced by the wrapping operation. A recorruption-based self-reconstruction loss in the gradient domain is proposed to mitigate the adverse effects of label noise, complemented with a self-distillation loss for improved generalization. Additionally, by unfolding a variational model of PU that utilizes wrapped gradients of wrapped phases for its data-fitting term, we develop a deep unrolling network that encodes physics of phase wrapping and incorporates special treatments on outliers. In the experiments on three types of phase data, our approach outperforms existing GT-free methods and competes well against the supervised ones.