A multimode fiber represents the ultimate limit in miniaturization of imaging endoscopes. However, such a miniaturization usually comes as a cost of a low spatial resolution and a long acquisition time. Here we propose a fast superresolution-fiber-imaging technique employing compressive sensing through a multimode fiber with a data-driven machine-learning framework. We implement a generative adversarial network (GAN) to explore the sparsity inherent to the model and provide compressive reconstruction images that are not sparse in a representation basis. The proposed method outperforms other widespread compressive imaging algorithms in terms of both image quality and noise robustness. We experimentally demonstrate machine-learning ghost imaging below the diffraction limit at a sub-Nyquist speed through a thin multimode fiber probe. We believe that this work has great potential in applications in various fields ranging from biomedical imaging to remote sensing.