The determination of Parton Distribution Functions (PDFs) from data is a typical example of an inverse problem, i.e. the reconstruction of a function from a linited set of data points. The details of the result depend on the methodology used for the solution. We introduce a stochastic framework to discuss inverse problems and shed some light on the relations between different methodologies. The framework is equally suited for extracting PDFs from lattice data, or spectral densities from Euclidean correlators.