Exploring the Intrinsic Geometry of Diffusion Models with Constrained Inverse Kinematics
The study tested if diffusion models can recover geometric structure in constrained inverse kinematics (IK), a setting with known geometry. Using two robots, the UR5 and Franka, trained models across seven constraint families showed that the recovered intrinsic dimension matches the analytical degrees of freedom. Furthermore, linear interpolation in latent space keeps generated solutions close to the constraint manifold, proving the model captures richer geometric structure than just its dimension.