We present a new method for real-time non-rigid dense correspondence between point clouds based on structured shape construction. Our method, termed Deep Point Correspondence (DPC), requires a fraction of the training data compared to previous techniques and presents better generalization capabilities. Until now, two main approaches have been suggested for the dense correspondence problem. The first is a spectral-based approach that obtains great results on synthetic datasets but requires mesh connectivity of the shapes and long inference processing time while being unstable in real-world scenarios. The second is a spatial approach that uses an encoder-decoder framework to regress an ordered point cloud for the matching alignment from an irregular input. Unfortunately, the decoder brings considerable disadvantages, as it requires a large amount of training data and fails to generalize well in cross-dataset evaluations. DPC's novelty lies in its lack of a decoder component. Instead, we use latent similarity and the input coordinates themselves to construct the point cloud and determine correspondence, replacing the coordinate regression, as done by the decoder. Extensive experiments show that our construction scheme leads to a performance boost in comparison to recent state-of-the-art correspondence methods.