Not yet reviewed by Pith; the record is open.

Learning from demonstrations faces challenges in generalizing beyond the training data and often lacks collision awareness. This paper introduces Lan-o3dp, a language-guided object-centric diffusion policy framework that can adapt to unseen situations such as cluttered scenes, shifting camera views, and ambiguous similar objects while offering training-free collision avoidance and achieving a high success rate with few demonstrations. We train a diffusion model conditioned on 3D point clouds of task-relevant objects to predict the robot's end-effector trajectories, enabling it to complete the tasks. During inference, we incorporate cost optimization into denoising steps to guide the generated trajectory to be collision-free. We leverage open-set segmentation to obtain the 3D point clouds of related objects. We use a large language model to identify the target objects and possible obstacles by interpreting the user's natural language instructions. To effectively guide the conditional diffusion model using a time-independent cost function, we proposed a novel guided generation mechanism based on the estimated clean trajectories. In the simulation, we showed that diffusion policy based on the object-centric 3D representation achieves a much higher success rate (68.7%) compared to baselines with simple 2D (39.3%) and 3D scene (43.6%) representations across 21 challenging RLBench tasks with only 40 demonstrations. In real-world experiments, we extensively evaluated the generalization in various unseen situations and validated the effectiveness of the proposed zero-shot cost-guided collision avoidance.