Homodyne X-ray diffraction signals produced by classical light and classical detectors are given by the modulus square of the charge density in momentum space vertical bar sigma(q)vertical bar(2), missing its phase, which is required in order to invert the signal to real space. We show that quantum detection of the radiation field yields a linear diffraction pattern that reveals sigma(q) itself, including the phase. We further show that repeated diffraction measurements with variable delays constitute a novel multidimensional measure of spontaneous charge-density fluctuations. Classical diffraction, in contrast, only reveals a subclass of even-order correlation functions. Simulations of two-dimensional signals obtained by two diffraction events are presented for the amino acid cysteine.