Infrared (IR) spectroscopy of molecular vibrations provides insight into molecular structure, coupling, and dynamics. However, picosecond scale intermolecular and intramolecular many-body interactions, nonradiative relaxation, absorption, and thermalization typically dominate over IR spontaneous emission. We demonstrate how coupling to a resonant IR antenna can enhance spontaneous emission of molecular vibrations. Using time-domain nanoprobe spectroscopy we observe an up to 50% decrease in vibrational dephasing time T_{2,vib}, based on the coupling-induced population decay with T_{κ}≃550 fs and an associated Purcell factor of >10^{6}. This rate enhancement of the spontaneous emission of antenna-coupled molecular vibrations opens new avenues for IR coherent control, quantum information processing, and quantum chemistry.