Controllable layout generation aims at synthesizing plausible arrangement of element bounding boxes with optional constraints, such as type or position of a specific element. In this work, we try to solve a broad range of layout generation tasks in a single model that is based on discrete state-space diffusion models. Our model, named Lay-outDM, naturally handles the structured layout data in the discrete representation and learns to progressively infer a noiseless layout from the initial input, where we model the layout corruption process by modality-wise discrete diffusion. For conditional generation, we propose to inject layout constraints in the form of masking or logit adjustment during inference. We show in the experiments that our Lay-outDM successfully generates high-quality layouts and outperforms both task-specific and task-agnostic baselines on several layout tasks. 1 1 Please find the code and models at: https://cyberagentailab.github.io/layout-drn.