Most of the known stochastic sentence generators use syntactically annotated corpora, performing the projection to the surface in one stage. However, in full-fledged text generation, sentence realization usually starts from semantic (predicate-argument) structures. To be able to deal with semantic structures, stochastic generators require semantically annotated, or, even better, multilevel annotated corpora. Only then can they deal with such crucial generation issues as sentence planning, linearization and morphologization. Multilevel annotated corpora are increasingly available for multiple languages. We take advantage of them and propose a multilingual deep stochastic sentence realizer that mirrors the state-ofthe-art research in semantic parsing. The realizer uses an SVM learning algorithm. For each pair of adjacent levels of annotation, a separate decoder is defined. So far, we evaluated the realizer for Chinese, English, German, and Spanish.