Belief Propagation as Diffusion

Message-passing algorithms such as belief propagation (BP) are parallel computing schemes that try to estimate the marginals of a high dimensional probability distribution. They are used in various areas involving the statistics of a large number of interacting random variables, such as computational thermodynamics [5, 10], artificial intelligence [11, 21, 15], computer vision [18] and communications processing [3, 4]. We have shown the existence of a non-linear correspondence between BP algorithms and discrete integrators of a new form of continuous-time diffusion equations on belief networks [13, 14].