Automatic layout generation is a fundamental problem in graphic design. Although recent diffusion-based models have achieved state-of-the-art FID scores, they underperform on alignment compared to earlier transformer-based models. In this work, we propose the LAyout Constraint diffusion modEl (LACE), a unified model for unconditional and conditional layout generation tasks in a continuous space. Compared with existing methods that use discrete diffusion models, continuous state space enables the incorporation of aesthetic constraint functions in training for enhanced visual quality. For conditional generation, LACE incorporates layout conditions via masked input throughout the training and testing phases. Experiment results show that LACE outperforms existing state-of-the-art baselines and produces visually plausible layouts.