Abstract: Robots operating in human environments must be able to rearrange objects into semantically-meaningful configurations, even if these objects are previously unseen. In this work, we focus on the problem of building physically-valid structures without step-by-step instructions. We propose StructDiffusion, which combines a diffusion model and an object-centric transformer to construct structures given partial-view point clouds and high-level language goals, such as “set the table”. Our method can perform multiple challenging language-conditioned multi-step 3D planning tasks using one model. StructDiffusion even improves the success rate of assembling physically-valid structures out of unseen objects by on average 16% over an existing multi-modal transformer model trained on specific structures. We show experiments on held-out objects in both simulation and on real-world rearrangement tasks. Importantly, we show how integrating both a diffusion model and a collision-discriminator model allows for improved generalization over other methods when rearranging previously-unseen objects.