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Multi-objective optimization problems are ubiquitous in robotics, e.g., theoptimization of a robot manipulation task requires a joint consideration ofgrasp pose configurations, collisions and joint limits. While some demands canbe easily hand-designed, e.g., the smoothness of a trajectory, severaltask-specific objectives need to be learned from data. This work introduces amethod for learning data-driven SE(3) cost functions as diffusion models.Diffusion models can represent highly-expressive multimodal distributions andexhibit proper gradients over the entire space due to their score-matchingtraining objective. Learning costs as diffusion models allows their seamlessintegration with other costs into a single differentiable objective function,enabling joint gradient-based motion optimization. In this work, we focus onlearning SE(3) diffusion models for 6DoF grasping, giving rise to a novelframework for joint grasp and motion optimization without needing to decouplegrasp selection from trajectory generation. We evaluate the representationpower of our SE(3) diffusion models w.r.t. classical generative models, and weshowcase the superior performance of our proposed optimization framework in aseries of simulated and real-world robotic manipulation tasks againstrepresentative baselines.

SE(3)-DiffusionFields: Learning smooth cost functions for joint grasp and motion optimization through diffusion