Abstract. This paper presents a deep architecture for dense semantic correspondence, called pyramidal affine regression networks (PARN), that estimates locally-varying affine transformation fields across images. To deal with intra-class appearance and shape variations that commonly exist among different instances within the same object category, we leverage a pyramidal model where affine transformation fields are progressively estimated in a coarse-to-fine manner so that the smoothness constraint is naturally imposed within deep networks. PARN estimates residual affine transformations at each level and composes them to estimate final affine transformations. Furthermore, to overcome the limitations of insufficient training data for semantic correspondence, we propose a novel weakly-supervised training scheme that generates progressive supervisions by leveraging a correspondence consistency across image pairs. Our method is fully learnable in an end-to-end manner and does not require quantizing infinite continuous affine transformation fields. To the best of our knowledge, it is the first work that attempts to estimate dense affine transformation fields in a coarse-to-fine manner within deep networks. Experimental results demonstrate that PARN outperforms the state-of-the-art methods for dense semantic correspondence on various benchmarks.