Rearranging objects is an essential skill for robots. To quickly teach robots new rearrangements tasks, we would like to generate training scenarios from high-level specifications that define the relative placement of objects for the task at hand. Ideally, to guide the robot's learning we also want to be able to rank these scenarios according to their difficulty. Prior work has shown how generating diverse scenario from specifications and providing the robot with easy-to-difficult samples can improve the learning. Yet, existing scenario generation methods typically cannot generate diverse scenarios while controlling their difficulty. We address this challenge by conditioning generative models on spatial logic specifications to generate spatially-structured scenarios that meet the specification and desired difficulty level. Our experiments showed that generative models are more effective and data-efficient than rejection sam-pling and that the spatially-structured scenarios can drastically improve training of downstream tasks by orders of magnitude.