The eigenmodes of spin diffusion provide a mathematical solution to the diffusion equation and the eigenmode spectrum can be used to characterize the internal space of porous media. The dynamics of these eigenmodes is affected by the presence of an inhomogeneous magnetic field inside the pores. In this paper we examine the behavior of the diffusion eigenmodes as a function of the spatially dependent encoding phase due to the inhomogeneous internal field. We show that in the limit of weak phase encoding, the first diffusion modes are predominantly excited. In this regime the excited signal is found to be linearly proportional to the encoding phase and the eigenmode spectrum reflects the pore size distribution. When the encoding phase is larger than 2 pi, the spectrum can be dominated by the higher eigenmodes.