Since the paradigm shift in 2009 from pseudo-thermal ghost imaging (GI) to computational GI using a spatial light modulator, computational GI has enabled image formation via a single-pixel detector and thus has a cost-effective advantage in some unconventional wave bands. In this Letter, we propose an analogical paradigm known as computational holographic ghost diffraction (CH-GD) to shift ghost diffraction (GD) from classical to computational by using self-interferometer-assisted measurement of field correlation functions rather than intensity correlation functions. More than simply "seeing" the diffraction pattern of an unknown complex volume object with single-point detectors, CH-GD can retrieve the diffracted light field's complex amplitude and can thus digitally refocus to any depth in the optical link. Moreover, CH-GD has the potential to obtain the multimodal information including intensity, phase, depth, polarization, and/or color in a more compact and lensless manner.