Existing deep hierarchical topic models are able to extract semantically meaningful topics from a text corpus in an unsupervised manner and automatically organize them into a topic hierarchy. However, it is unclear how to incorporate prior belief such as knowledge graph to guide the learning of the topic hierarchy. To address this issue, we introduce TopicNet as a deep hierarchical topic model that can inject prior structural knowledge as inductive bias to influence the learning. TopicNet represents each topic as a Gaussian-distributed embedding vector, projects the topics of all layers into a shared embedding space, and explores both the symmetric and asymmetric similarities between Gaussian embedding vectors to incorporate prior semantic hierarchies. With a variational auto-encoding inference network, the model parameters are optimized by minimizing the evidence lower bound and supervised loss via stochastic gradient descent. Experiments on widely used benchmark show that TopicNet outperforms related deep topic models on discovering deeper interpretable topics and mining better document representations.