Title: BAT-Chain: Bayesian-Aware Transport Chain for Topic Hierarchies Discovery. Abstract: Topic modeling has been an important tool for text analysis. Originally, topics discovered by a model are usually assumed to be independent. However, as a semantic representation of a concept, a topic is naturally related to others, which motivates the development of learning hierarchical topic structure. Most existing Bayesian models are designed to learn hierarchical structure, but they need non-trivial posterior inference. Although the recent transport-based topic models bypass the posterior inference, none of them considers deep topic structures. In this paper, we interpret document as its word embeddings and propose a novel Bayesian-aware transport chain to discover multi-level topic structures, where each layer learns a set of topic embeddings and the document hierarchical representations are defined as a series of empirical distributions according to the topic proportions and corresponding topic embeddings. To fit such hierarchies, we develop an upward-downward optimizing strategy under the recent conditional transport theory, where document information is first transported via the upward path, and then its hierarchical representations are refined by the downward path under the Bayesian perspective. Extensive experiments on text corpora show that our approach enjoys superior modeling accuracy and interpretability. Moreover, we also conduct experiments on learning hierarchical visual topics from images, which demonstrate the adaptability and flexibility of our method.