Abstract: Recent progress in sentence embedding, which represents a sentence's meaning as a point in a vector space, has achieved high performance on several tasks such as the semantic textual similarity (STS) task. However, a sentence representation cannot adequately express the diverse information that sentences contain: for example, such representations cannot naturally handle asymmetric relationships between sentences. This paper proposes GaussCSE, a Gaussian-distribution-based contrastive learning framework for sentence embedding that can handle asymmetric inter-sentential relations, as well as a similarity measure for identifying entailment relations. Our experiments show that GaussCSE achieves performance comparable to that of previous methods on natural language inference (NLI) tasks, and that it can estimate the direction of entailment relations, which is difficult with point representations.