Owing to its unique penetrating power and high-resolution capability, X-ray imaging has been an irreplaceable tool since its discovery. Despite the significance, the resolution of X-ray imaging has largely been limited by the technical difficulties on X-ray lens making. Various lensless imaging methods have been proposed, but are yet relying on multiple measurements or additional constraints on measurements or samples. Here we present coherent speckle-correlation imaging (CSI) using a designed X-ray diffuser. CSI has no prerequisites for samples or measurements. Instead, from a single shot measurement, the complex sample field is retrieved based on the pseudorandomness of the speckle intensity pattern, ensured through a diffuser. We achieve a spatial resolution of 13.9 nm at 5.46 keV, beating the feature size of the diffuser used (300 nm). The high-resolution imaging capability is theoretically explained based on fundamental and practical limits. We expect the CSI to be a versatile tool for navigating the unexplored world of nanometer.