We propose a face difference model that decomposes face difference into three components, intrinsic difference, transformation difference, and noise. Using the face difference model and a detailed subspace analysis on the three components we develop a unified framework for subspace analysis. Using this framework we discover the inherent relationship among different subspace methods and their unique contributions to the extraction of discriminating information from the face difference. This eventually leads to the construction of a 3D parameter space that uses three subspace dimensions as axis. Within this parameter space, we develop a unified subspace analysis method that achieves better recognition performance than the standard subspace methods on over 2000 face images from the FERET database.