Rao–Blackwellization is an approximation technique for probabilistic in- ference that ﬂexibly combines exact inference with sampling. It is useful in models where conditioning on some of the variables leaves a sim- pler inference problem that can be solved tractably. This paper presents Sample Propagation, an efﬁcient implementation of Rao–Blackwellized approximate inference for a large class of models. Sample Propagation tightly integrates sampling with message passing in a junction tree, and is named for its simple, appealing structure: it walks the clusters of a junction tree, sampling some of the current cluster’s variables and then passing a message to one of its neighbors. We discuss the application of Sample Propagation to conditional Gaussian inference problems such as switching linear dynamical systems.