With the development of pre-trained language models, remarkable success has been witnessed in dialogue understanding (DU). However, current DU approaches usually employ independent models for each distinct DU task, without considering shared knowledge across different DU tasks. In this paper, we propose a unified generative dialogue understanding framework, named UniDU, to achieve effective information exchange across diverse DU tasks. Here, we reformulate all DU tasks into a unified prompt-based generative model paradigm. More importantly, a novel model-agnostic multi-task training strategy (MATS) is introduced to dynamically adapt the weights of diverse tasks for best knowlege sharing during training, based on the nature and available data of each task. Experiments on ten DU datasets covering five fundamental DU tasks show that the proposed UniDU framework largely outperforms task-specific well-designed methods on all tasks. MATS also reveals the knowledge sharing structure of these tasks. Finally, UniDU obtains promising performance on unseen dialogue domain, showing great potential of generalization.