Though one normally thinks of single-molecule diffraction studies as tools for eliciting molecular geometry, molecular diffraction patterns are really the Fourier transforms of complete molecular wave functions. There is thus at least the possibility of imaging the vibrational wave functions of polyatomic molecules by means of a pump-probe diffraction experiment: the pump laser could prepare a specific vibrational state and an electron or x-ray could then be diffracted off the molecule some short time later. The present paper develops the general theory of diffraction signatures for individual vibrational wave functions in polyatomic molecules and investigates the feasibility of seeing such signatures experimentally using the example of a linear triatomic molecule modeled after CS2. Although aligned molecules in specific vibrational quantum states turn out to exhibit very characteristic diffraction signatures, the signatures of the vibrational wave functions are partially washed out for the complete isotropy expected from gas phase molecules. Nonetheless, it is possible to design a diffraction experiment using a pump-dump sequence with a polarized laser beam which will select a nonisotropic sample of vibrationally excited molecules. We show that the resulting level of anisotropy should enhance the diffraction signature, helping to distinguish different vibrational components. These model calculations therefore suggest the possibility of observing the dynamics of vibrational wave packets using experimentally realizable diffraction techniques.