In this paper we characterize the conditionallaw of the ith coordinate of an infinite-dimensional diffusion process with respect to the othersIf the interaction is given by a smooth gradient system of finite range, the conditional probability is determined in a robust form as the law of a stochastic differential equation with smooth and bounded drift and initial measure. Additionally the conditional law is shown to be Lipschitz continuous inwith respect to the Vasserstein metric on C[iX 1]