Hitomi observations of Perseus with the Soft X-ray Spectrometer (SXS) provide a high-resolution look at the 3.5 keV feature reported by multiple groups in the Perseus cluster. The Hitomi spectrum—which involves the sum of diffuse cluster emission and the pointlike central active galactic nucleus (AGN)—does not show any excess at E∼3.5  keV, giving an apparent inconsistency with previous observations of excess diffuse emission. We point out that 2009 Chandra data reveals a strong dip in the AGN spectrum at E=(3.54±0.02)  keV (cluster frame)—the identical energy to the diffuse excess observed by XMM-Newton. Scaling this dip to the 2016 AGN luminosity and adding it to the diffuse XMM-Newton excess, this predicts an overall dip in the SXS field of view of (-5.9±4.4)×10-6  ph cm-2 s-1 at E=3.54  keV—a precise match to the Hitomi data when broadened by the dark matter virial velocity. We describe models of fluorescent dark matter that can reproduce this physics, in which dark matter absorbs and then reemits 3.5 keV photons emitted from the central AGN.