This paper presents a detailed analysis of magnetic flux losses in explosive driven flux compression generators. Magnetic field diffusion into generator conductors can lead to substantial losses. A study of linear diffusion is therefore the major subject treated in this paper. Diffusion analysis is considerably complicated by the presence of moving conductors and the compression of magnetic flux. Consequently, the text is treated in a tutorial fashion. This is particularly true in the earlier parts of the paper, where formulation of the basic equations, various conservation laws, and problem solutions are treated in considerable detail. A point of departure from earlier treatments of the subject is the addition of external circuits to the generators. It is shown that the influence of these circuits enters into the boundary conditions for the diffusion equations. A number of analytic solutions are obtained for various external circuits.