With the recent breakthrough of highly accurate structure prediction methods, there has been a rapid growth of available protein structures. Efficient methods are needed to infer structural similarity within these datasets. We present an end-to-end alignment method, called SWAMPNN, that takes as input the 3D coordinates of a protein pair and outputs a structural alignment. We show that the model is able to recapitulate TM-align alignments while running faster and is more accurate than Foldseek on the alignment task while being comparable for classification.