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Exemplar-based image translation establishes dense correspondences between a conditional input and an exemplar (from two different domains) for leveraging detailed exemplar styles to achieve realistic image translation. Existing work builds the cross-domain correspondences implicitly by minimizing feature-wise distances across the two domains. Without explicit exploitation of domain-invariant features, this approach may not reduce the domain gap effectively which often leads to sub-optimal correspondences and image translation. We design a Marginal Contrastive Learning Network (MCL-Net) that explores contrastive learning to learn domain-invariant features for realistic exemplar-based image translation. Specifically, we design an innovative marginal contrastive loss that guides to establish dense correspondences explicitly. Nevertheless, building correspondence with domain-invariant semantics alone may impair the texture patterns and lead to degraded texture generation. We thus design a Self-Correlation Map (SCM) that incorporates scene structures as auxiliary information which improves the built correspondences substantially. Quantitative and qualitative experiments on multifarious image translation tasks show that the proposed method outperforms the state-of-the-art consistently.