Generative modeling via diffusion-based models has been achieving state-of-the-art results on various generation tasks. Most existing diffusion models, however, are limited to a single-generation modeling. Can we generalize diffusion models with the ability of multi-task generative training for more generalizable modeling? In this paper, we propose a principled way to define a diffusion model for this purpose by constructing a unified multi-task diffusion model in a common {\em diffusion space}. We define the forward diffusion process to be driven by an information aggregation from multiple types of task-data, {\it e.g.}, images for a generation task and labels for a classification task. In the reverse process, we enforce information sharing by parameterizing a shared backbone denoising network with additional task-specific decoder heads. Such a structure can simultaneously learn to generate different types of multi-task data with a multi-task loss, which is derived from a multi-task variational lower bound that generalizes the standard diffusion model. We propose several multi-task generation settings to verify our framework, including image transition, masked-image training, joint image-label and joint image-representation generative modeling. Extensive experimental results on ImageNet indicate the effectiveness of our framework for various multi-task generative modeling, which we believe is an important research direction worthy of more future explorations.