In this paper we develop a new formulation of probabilistic relaxation labeling for the task of data classification using the theory of diffusion processes on graphs. The state space of our process as the nodes of a support graph which represent potential object-label assignments. The edge-weights of the support graph encode data-proximity and label consistency information. The state-vector of the diffusion process represents the object-label probabilities. The state vector evolves with time according to the Fokker-Planck equation.We show how the solution state vector can be estimated using the spectrum of the Laplacian matrix for the weighted support graph. Experiments on various data clustering tasks show effectiveness of our new algorithm.