X-ray phase contrast is a promising breast image modality. This technique is capable of simultaneously providing three types of images: absorption, differential phase contrast (DPC) and dark-field (DF) images, allowing to obtain complementary information from each one. However, the Talbot-Lau interferometer, the device used to acquire this type of images, can yield Moiré artifacts in the corresponding images. The aim of this work is to introduce a deep learning approach, using a generative adversarial network, in particular the pix2pix neural network, to reduce Moiré artifacts efficiently. Our approach was tested using simulated DPC and DF images obtained from the INbreast dataset. Moiré and mammography-based images are fused using a novel approach which aims to eliminate the bias yielded by the traditional one. Results shows a significant image quality improvement for the DF dataset, reaching a structural similarity (SSIM) index of \(SSIM=0.96\pm 0.02\) , in average, after applying the neural network. However, under the same training conditions, the denoised DPC images do not show such a clear improvement, yielding checkerboard and discontinuity artifacts.