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Semantic editing of images is the fundamental goal of computer vision.Although deep learning methods, such as generative adversarial networks (GANs),are capable of producing high-quality images, they often do not have aninherent way of editing generated images semantically. Recent studies haveinvestigated a way of manipulating the latent variable to determine the imagesto be generated. However, methods that assume linear semantic arithmetic havecertain limitations in terms of the quality of image editing, whereas methodsthat discover nonlinear semantic pathways provide non-commutative editing,which is inconsistent when applied in different orders. This study proposes anovel method called deep curvilinear editing (DeCurvEd) to determine semanticcommuting vector fields on the latent space. We theoretically demonstrate thatowing to commutativity, the editing of multiple attributes depends only on thequantities and not on the order. Furthermore, we experimentally demonstratethat compared to previous methods, the nonlinear and commutative nature ofDeCurvEd facilitates the disentanglement of image attributes and provideshigher-quality editing.

Deep Curvilinear Editing: Commutative and Nonlinear Image Manipulation for Pretrained Deep Generative Model