jats:titleAbstract</jats:title>jats:pMedical image reconstruction and synthesis are critical for imaging quality, disease diagnosis and treatment. Most of the existing generative models ignore the fact that medical imaging usually occurs in the acquisition domain, which is different from, but associated with, the image domain. Such methods exploit either single-domain or dual-domain information and suffer from inefficient information coupling across domains. Moreover, these models are usually designed specifically and not general enough for different tasks. Here we present a generalized dual-domain generative framework to facilitate the connections within and across domains by elaborately-designed hierarchical consistency constraints. A multi-stage learning strategy is proposed to construct hierarchical constraints effectively and stably. We conducted experiments for representative generative tasks including low-dose PET/CT reconstruction, CT metal artifact reduction, fast MRI reconstruction, and PET/CT synthesis. All these tasks share the same framework and achieve better performance, which validates the effectiveness of our framework. This technology is expected to be applied in clinical imaging to increase diagnosis efficiency and accuracy.</jats:p>