What Do You Need for Diverse Trajectory Stitching in Diffusion Planning?

In planning, stitching is an ability of algorithms to piece together sub-trajectories of data they are trained on to generate new and diverse behaviours. While stitching is historically a strength of offline reinforcement learning, recent generative behavioural cloning (BC) methods have also shown proficiency at stitching. However, the main factors behind this are poorly understood, hindering the development of new algorithms that can reliably stitch. Focusing on diffusion planners trained via BC, we find two properties are needed to compose: \emph{positional equivariance} and \emph{local receptiveness}. We use these two properties to explain architecture, data, and inference choices in existing generative BC methods based on diffusion planning, including replanning frequency, data augmentation, and data scaling. Experimental comparisions show that (1) while locality is more important than positional equivariance in creating a diffusion planner capable of composition, both are crucial (2) enabling these properties through relatively simple architecture choices can be competitive with more computationally expensive methods such as replanning or scaling data, and (3) simple inpainting-based guidance can guide architecturally compositional models to enable generalization in goal-conditioned settings.