Lights, Camera, Axion: Tracing Axions from Supernovae in the Diffuse $\gamma$-ray Sky

Axions produced copiously in core-collapse supernovae can convert into photons as they propagate through various astrophysical magnetic fields. The cumulative emission from the cosmic population of supernovae can therefore generate a diffuse gamma-ray signal through axion-photon conversion. In this work, we develop a comprehensive framework to compute the diffuse gamma-ray flux by modeling axion production in supernovae and, \textit{for the first time}, consistently accounting for their conversion into photons across all relevant magnetic field environments - progenitor, host galaxy, intergalactic medium, and the Milky Way - together with an updated cosmic star formation rate. Using measurements of the diffuse gamma-ray sky from COMPTEL, EGRET, and \textit{Fermi}-LAT, we derive competitive constraints on the axion-photon coupling over a wide range of axion masses. We further forecast the sensitivity of upcoming MeV gamma-ray telescopes to this diffuse signal using a Fisher forecast analysis.