We introduce an approach to integrate bi-directional contexts in a generative tree model by means of structured transductions. We show how this can be efficiently realized as the composition of a top-down and a bottom-up generative model for trees, that are trained independently within a circular encoding-decoding scheme. The resulting input-driven generative model is shown to capture information concerning bi-directional contexts within its state-space. An experimental evaluation using the Jaccard generative kernel for trees is presented, indicating that the approach can achieve state of the art performance on tree classification benchmarks.