Measurements of neural responses to identically repeated experimental events often exhibit large amounts of variability. This noise is distinct from signal, operationally defined as the average expected response across repeated trials for each given event. Accurately distinguishing signal from noise is important, as each is a target that is worthy of study (many believe noise reflects important aspects of brain function) and it is important not to confuse one for the other. Here, we describe a principled modeling approach in which response measurements are explicitly modeled as the sum of samples from multivariate signal and noise distributions. In our proposed method -- termed Generative Modeling of Signal and Noise (GSN) -- the signal distribution is estimated by subtracting the estimated noise distribution from the estimated data distribution. We validate GSN using ground-truth simulations and show that it compares favorably with related methods. We also demonstrate the application of GSN to empirical fMRI data to illustrate a simple consequence of GSN: by disentangling signal and noise components in neural responses, GSN denoises principal components analysis and improves estimates of dimensionality. We end by discussing a promising extension of GSN that provides denoised response estimates for individual trials and a real-world application of GSN to a condition-rich 7T fMRI language experiment.