As an effective way to integrate the information contained in multiple medical images under different modalities, medical image synthesis and fusion have emerged in various clinical applications such as disease diagnosis and treatment planning. In this paper, an invertible and variable augmented network (iVAN) is proposed for medical image synthesis and fusion. In iVAN, the channel number of the network input and output is the same through variable augmentation technology, and data relevance is enhanced, which is conducive to the generation of characterization information. Meanwhile, the invertible network is used to achieve the bidirectional inference processes. Empowered by the invertible and variable augmentation schemes, iVAN not only be applied to the mappings of multi-input to one-output and multi-input to multi-output, but also to the case of one-input to multi-output. Experimental results demonstrated superior performance and potential task flexibility of the proposed method, compared with existing synthesis and fusion methods.