Quasar Factor Analysis (QFA) is an unsupervised probabilistic model for predicting quasar continua directly from spectroscopic data. It combines factor analysis (FA) with physical priors on the intergalactic medium (IGM) absorption.In the FA component, the model assumes the intrinsic quasar spectrum is a linear combination of a small number of latent factors, each representing a spectral component. The factor loadings for a given quasar encode how much each factor contributes to its spectrum.The IGM priors impose constraints on the possible continuum predictions based on our knowledge of IGM absorption at different wavelengths. This aids in disentangling the intrinsic spectrum from IGM effects.QFA is fit to data by maximizing the likelihood of the observed spectra under the FA model subject to the IGM constraints. This results in a posterior distribution over the latent factors and continuum predictions.After fitting, QFA can predict the intrinsic continuum for new quasar spectra based on their estimated factor loadings. The nonlinear IGM constraints improve accuracy compared to standard linear factor models.Additionally, QFA provides interpretable latent factors revealing the main sources of spectral variance in the quasar population. The generative modeling approach also enables robust outlier detection.QFA overcomes limitations of methods relying on a small set of high-quality reference spectra. By directly modeling the full database, it better captures the diversity of quasar properties.