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Recent image-to-image (I2I) translation algorithms focus on learning the mapping from a source to a target domain. However, the continuous translation problem that synthesizes intermediate results between two domains has not been well-studied in the literature. Generating a smooth sequence of intermediate results bridges the gap of two different domains, facilitating the morphing effect across domains. Existing I2I approaches are limited to either intra-domain or deterministic inter-domain continuous translation. In this work, we present an effectively signed attribute vector, which enables continuous translation on diverse mapping paths across various domains. In particular, we introduce a unified attribute space shared by all domains that utilize the sign operation to encode the domain information, thereby allowing the interpolation on attribute vectors of different domains. To enhance the visual quality of continuous translation results, we generate a trajectory between two sign-symmetrical attribute vectors and leverage the domain information of the interpolated results along the trajectory for adversarial training. We evaluate the proposed method on a wide range of I2I translation tasks. Both qualitative and quantitative results demonstrate that the proposed framework generates more high-quality continuous translation results against the state-of-the-art methods.