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Medical image translation (e.g. CT to MR) is a challenging task as it requires I) faithful translation of domain-invariant features (e.g. shape information of anatomical structures) and II) realistic synthesis of target-domain features (e.g. tissue appearance in MR). In this work, we propose Manifold Disentanglement Generative Adversarial Network (MDGAN), a novel image translation framework that explicitly models these two types of features. It employs a fully convolutional generator to model domain-invariant features, and it uses style codes to separately model target-domain features as a manifold. This design aims to explicitly disentangle domain-invariant features and domain-specific features while gaining individual control of both. The image translation process is formulated as a stylisation task, where the input is "stylised" (translated) into diverse target-domain images based on style codes sampled from the learnt manifold. We test MDGAN for multi-modal medical image translation, where we create two domain-specific manifold clusters on the manifold to translate segmentation maps into pseudo-CT and pseudo-MR images, respectively. We show that by traversing a path across the MR manifold cluster, the target output can be manipulated while still retaining the shape information from the input.