Being able to automatically discover synonymous entities in an open-world setting benefits various tasks such as entity disambiguation or knowledge graph canonicalization. Existing works either only utilize entity features, or rely on structured annotations from a single piece of context where the entity is mentioned. To leverage diverse contexts where entities are mentioned, in this paper, we generalize the distributional hypothesis to a multi-context setting and propose a synonym discovery framework that detects entity synonyms from free-text corpora with considerations on effectiveness and robustness. As one of the key components in synonym discovery, we introduce a neural network model SynonymNet to determine whether or not two given entities are synonym with each other. Instead of using entities features, SynonymNet makes use of multiple pieces of contexts in which the entity is mentioned, and compares the context-level similarity via a bilateral matching schema. Experimental results demonstrate that the proposed model is able to detect synonym sets that are not observed during training on both generic and domain-specific datasets: Wiki+Freebase, PubMed+UMLS, and MedBook+MKG, with up to 4.16% improvement in terms of Area Under the Curve and 3.19% in terms of Mean Average Precision compared to the best baseline method.