The vast majority of nonlinear optical spectroscopies work in an integrated mode, namely they use the mean-value signal, properly averaged over several stroboscopic repetitions. While ensuring an adequate signal-to-noise ratio, this approach relies strongly on pulse-to-pulse consistency and has thus motivated significant efforts in pursuit of perfect experimental stability. By contrast, we have developed a fundamentally different approach, named Femtosecond Covariance Spectroscopy (FCS), which identifies noise as a powerful and unique asset to access information that standard mean-value experiments miss. FCS is based on covariance rather than mean-value observables and relies on the study of multimode quantum correlations imprinted on stochastic ultrashort pulses by light-matter interactions. As a proof of principle, we have successfully applied such approach to the study of Raman-active vibrational modes excited through Impulsive Stimulated Raman Scattering (ISRS) in crystalline quartz. Nevertheless, the impact of FCS is not only limited to the field of condensed matter physics. Indeed, given the formal analogy between the quantum description of ISRS and optomechanical experiments, FCS could pave the way to a new generation of experiments in which the coupling between the electromagnetic field and the mechanical oscillator, could be reproduced by the interaction between light pulses and phonon modes.