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Frequency upconversion is a cornerstone of electromagnetic signal processing, analysis and detection. It is used to transfer energy and information from one frequency domain to another where transmission, modulation or detection is technically easier or more efficient. Optomechanical transduction is emerging as a flexible approach to coherent frequency upconversion; it has been successfully demonstrated for conversion from radio- and microwaves (kHz to GHz) to optical fields. Nevertheless, optomechanical transduction of multi-THz and mid-infrared signals remains an open challenge. Here, we utilize molecular cavity optomechanics to demonstrate upconversion of sub-microwatt continuous-wave signals at $\sim$32~THz into the visible domain at ambient conditions. The device consists in a plasmonic nanocavity hosting a small number of molecules. The incoming field resonantly drives a collective molecular vibration, which imprints an optomechanical modulation on a visible pump laser and results in Stokes and anti-Stokes upconverted Raman sidebands with sub-natural linewidth, indicating a coherent process. The nanocavity offers 13 orders of magnitude enhancement of upconversion efficiency per molecule compared to free space, with a measured phonon-to-photon internal conversion efficiency larger than $10^{-4}$ per milliwatt of pump power. Our results establish a flexible paradigm for optomechanical frequency conversion using molecular oscillators coupled to plasmonic nanocavities, whose vibrational and electromagnetic properties can be tailored at will using chemical engineering and nanofabrication., Comment: Includes Supplementary Material, 31 pages