Image registration is a very common procedure in dental applications for aligning images. Registration between pairs of images taken from different angles can improve diagnosis. Our study presents an edge-enhanced unsupervised deep learning (DL)-based deformable registration framework for aligning two-dimensional (2D) pairs of dental x-ray images. The proposed neural network is based on the combination of a U-Net like structure, which produces a displacement field, combined with spatial transformer networks, which produce the transformed image. The proposed structure is trained end-to-end by minimizing a weighted loss function consisting of three parts corresponding to image similarity, edge similarity, and registration restrictions. In this regard, the proposed edge specific loss enhances the unsupervised training of the registration framework without the need of supervision through anatomical structures. The proposed framework was applied to two datasets, a set of 104 x-ray images of mandibles, arranged in 2600 pairs for training and testing and a set of 17 pairs of pre- and post-operative reconstructed panoramic images. The proposed model outperformed both conventional registration methods and DL-based techniques for both qualitative and quantitative assessment, in most of the compared metrics concerning intensity similarity and edge distances. The proposed framework achieved accurate and fast deformable alignment of pairs of 2D dental radiographic images. The edge-based module of the loss function enhances the unsupervised learning by directing the network toward deformations that take into consideration the edges of the depicted objects (teeth, bone, and tissue), which are crucial in diagnosis.