This paper proposes a distance metric for documents. The proposed solution is to combine latent topics from topic models with the idea of using geometry from word embeddings to compute distances between pairs of documents (as in the WMD metric). First topics are computed, and WMD is performed at the topic level as opposed to the word level. The hypothesis presented is that modeling documents by their representative topics is better for highlighting differences despite the loss in resolution and is similar to how a person would do this task: breaking down each document into concepts, and then comparing the concepts. Since the topics are precomputed for a given corpus, speed up is gained at inference time when computing document similarities. The paper also reasons that since the topics are fewer, one gains interpretability from the proposed topic-level distance measure. The reviewers felt their concerns were addressed by the author response, and there is support for acceptance.