  Relativistic axions can be readily produced in a broad variety of transient
sources, such as axion star bosenova explosions, supernovae or even evaporating
primordial black holes. We develop a general framework describing the resulting
persistent diffuse axion background (D$a$B) due to accumulated axions from
historic transient events. We derive strong constraints on the D$a$B flux from
light axions $m\lesssim 10^{-3}\,{\rm eV}$ emitted from sources with energies
$\omega \gtrsim{\rm MeV}$ considering the non-observation of excess photons
associated with axion-photon coupling from experiments, including COMPTEL,
NuSTAR, XMM-Newton, INTEGRAL, EGRET and Fermi. Future searches in experiments
such as SKA, JWST, XRISM, Vera C. Rubin Observatory, AMEGO/e-ASTROGAM will
allow probing D$a$B and associated axion-photon couplings with unprecedented
sensitivity covering a wide range of possible source energies as low as
$0.1\,\mu$eV and multiple decades in axion masses. We highlight the differences
between astrophysical and dark sector sources of D$a$B. Further, we discuss
complementarity with direct detection as well as prospects for other D$a$B
searches. Our analysis demonstrates that D$a$B can act as a promising probe of
populations of axion emission sources as well as emission mechanisms.
