  Multi-objective optimization problems are ubiquitous in robotics, e.g., the
optimization of a robot manipulation task requires a joint consideration of
grasp pose configurations, collisions and joint limits. While some demands can
be easily hand-designed, e.g., the smoothness of a trajectory, several
task-specific objectives need to be learned from data. This work introduces a
method for learning data-driven SE(3) cost functions as diffusion models.
Diffusion models can represent highly-expressive multimodal distributions and
exhibit proper gradients over the entire space due to their score-matching
training objective. Learning costs as diffusion models allows their seamless
integration with other costs into a single differentiable objective function,
enabling joint gradient-based motion optimization. In this work, we focus on
learning SE(3) diffusion models for 6DoF grasping, giving rise to a novel
framework for joint grasp and motion optimization without needing to decouple
grasp selection from trajectory generation. We evaluate the representation
power of our SE(3) diffusion models w.r.t. classical generative models, and we
showcase the superior performance of our proposed optimization framework in a
series of simulated and real-world robotic manipulation tasks against
representative baselines.
