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We investigate the infrared (IR) emission of high-redshift ($z\sim 6$),highly star-forming (${ {\rm SFR} > 100}$ $M_{\rm \odot} {\rm yr}^{-1}$)galaxies, with/without Active Galactic Nuclei (AGN), using a suite ofcosmological simulations featuring dust radiative transfer. Synthetic SpectralEnergy Distributions (SEDs) are used to quantify the relative contribution ofstars/AGN to dust heating. In dusty (${M_{\rm d}\gtrsim 3\times 10^7 M_{\rm\odot}}$) galaxies, $\gtrsim 50-90 \%$ of the UV radiation is obscured by dustinhomogeneities on scales ${\gtrsim 100}$ pc. In runs with AGN, a clumpy, warm($\approx 250$ K) dust component co-exists with a colder ($\approx 60$ K) andmore diffuse one, heated by stars. Warm dust provides up to ${50 \%}$ of thetotal IR luminosity, but only $\lesssim 0.1 \%$ of the total mass content. TheAGN boosts the MIR flux by ${10-100 \times}$ with respect to star forminggalaxies, without significantly affecting the FIR. Our simulations successfullyreproduce the observed SED of bright (${M_{\rm UV}\sim -26}$) ${z\sim 6}$quasars, and show that these objects are part of complex, dust-rich mergingsystems, containing multiple sources (accreting BHs and/or star forminggalaxies) in agreement with recent HST and ALMA observations. Our results showthat the proposed ORIGINS missions will be able to investigate the MIRproperties of dusty star forming galaxies and to obtain good quality spectra ofbright quasars at $z\sim 6$. Finally, the MIR-to-FIR flux ratio of faint(${M_{\rm UV}\sim -24}$) AGN is ${>10\times}$ higher than for normal starforming galaxies. This implies that combined JWST/ORIGINS/ALMA observationswill be crucial to identify faint and/or dust-obscured AGN in the distantUniverse.

Infrared emission of $z \sim 6$ galaxies: AGN imprints