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We derive supernova (SN) bounds on muon-philic bosons, taking advantage ofthe recent emergence of muonic SN models. Our main innovations are to considerscalars $\phi$ in addition to pseudoscalars $a$ and to include systematicallythe generic two-photon coupling $G_{\gamma\gamma}$ implied by a muon triangleloop. This interaction allows for Primakoff scattering and radiative bosondecays. The globular-cluster bound $G_{\gamma\gamma}<0.67\times10^{-10}~{\rmGeV}^{-1}$ derived for axion-like particles carries over to the muonic Yukawacouplings as $g_a<3.1\times10^{-9}$ and $g_\phi< 4.6\times10^{-9}$ for$m_{a,\phi}\lesssim 100$ keV, so SN arguments become interesting mainly forlarger masses. If bosons escape freely from the SN core the main constraintsoriginate from SN1987A $\gamma$ rays and the diffuse cosmic $\gamma$-raybackground. The latter allows at most $10^{-4}$ of a typical total SN energy of$E_{\rm SN}\simeq3\times10^{53}$erg to show up as $\gamma$ rays, for$m_{a,\phi}\gtrsim 100$keV implying $g_a \lesssim 0.9\times10^{-10}$ and$g_\phi \lesssim 0.4\times10^{-10}$. In the trapping regime the bosons emergeas quasi-thermal radiation from a region near the neutrino sphere and match$L_\nu$ for $g_{a,\phi}\simeq 10^{-4}$. However, the $2\gamma$ decay is so fastthat all the energy is dumped into the surrounding progenitor-star matter,whereas at most $10^{-2}E_{\rm SN}$ may show up in the explosion. To suppressboson emission below this level we need yet larger couplings, $g_{a}\gtrsim2\times10^{-3}$ and $g_{\phi}\gtrsim 4\times10^{-3}$. Muonic scalars canexplain the muon magnetic-moment anomaly for $g_{\phi}\simeq 0.4\times10^{-3}$,a value hard to reconcile with SN physics despite the uncertainty of theexplosion-energy bound. For generic axion-like particles, this argument coversthe "cosmological triangle" in the $G_{a\gamma\gamma}$--$m_a$ parameter space.

Muonic Boson Limits: Supernova Redux