A processor-implemented method with data processing using a neural network includes: determining a first translated image by translating a first image based on a second image, the first image and a second image that having different distortions, such that a distortion of the first image corresponds to a distortion of the second image; determining a first retranslated image by translating the first translated image such that a distortion of the first translated image corresponds to a distortion of the first image; and training a first deformation field generator configured to determine a first relative deformation field that represents a relative deformation from the first image to the second image and a second deformation field generator configured to determine a second relative deformation field that represents a relative deformation from the second image to the first image, based on a loss between the first retranslated image and the first image.