We have modeled the fluorescent pumping of electronic and vibrational emissions of molecular hydrogen (H2) within diffuse molecular clouds that are illuminated by ultraviolet continuum radiation. Fluorescent line intensities are predicted for transitions at ultraviolet, infrared, and red visible wavelengths as functions of the gas density, the visual extinction through the cloud, and the intensity of the incident UV continuum radiation. The observed intensity in each fluorescent transition is roughly proportional to the integrated rate of H2 photodissociation along the line of sight Although the most luminous fluorescent emissions detectable from ground-based observatories lie at near-infrared wavelengths, we argue that the lower sky brightness at visible wavelengths makes the red fluorescent transitions a particularly sensitive probe. Fabry-Perot spectrographs of the type that have been designed to observe very faint diffuse Hα emissions are soon expected to yield sensitivities that will be adequate to detect H2 vibrational emissions from molecular clouds that are exposed to ultraviolet radiation no stronger than the mean radiation field within the Galaxy. Observations of red H2 fluorescent emission together with cospatial 21 cm H I observations could serve as a valuable probe of the gas density in diffuse molecular clouds.