The recent demonstration of a terahertz (THz) molecular gas laser pumped by a mid-infrared quantum cascade laser (QCL) has opened up new perspectives for this family of sources, traditionally relying on CO2-laser pumping. A so far open question concerning QCL-pumped THz molecular lasers (MLs) is related to their spectral purity. Indeed, assessing their frequency/phase noise is crucial for a number of applications potentially exploiting these sources as local oscillators. Here this question is addressed by reporting the measurement of the frequency noise power spectral density (PSD) of a THz ML pumped by a 10.3µm-wavelength QCL, and emitting 1mW at 1.1THz in continuous wave. This is achieved by beating the ML frequency with the 1080 th harmonic of the repetition rate of a 1560nm frequency comb. We find a frequency noise PSD < 10Hz 2 /Hz (-95dBc/Hz) at 100kHz from the carrier. To demonstrate the effect of the stability of the pump laser on the spectral purity of the THz emission we also measure the frequency noise PSD of a CO2-laser-pumped 2.5THz ML, reaching 0.1Hz 2 /Hz (-105dBc/Hz) at 40kHz from the carrier, limited by the frequency noise of the frequency comb harmonic. Finally, we show that it is possible to actively phase-lock the QCL-pumped molecular laser to the frequency comb repetition rate harmonic by controlling the QCL current, demonstrating a sub-Hz linewidth. 2Read less <