This work presents an efficient framework to generate a motion plan of a robot with high degrees of freedom (e.g., a humanoid robot). High dimensionality of the robot configuration space often leads to difficulties in utilizing the widely used motion planning algorithms, since the volume of the decision space increases exponentially with the number of dimensions. To handle complications arising from the large decision space, and to solve a corresponding motion planning problem efficiently, two key concepts are adopted in this work: First, the Gaussian process latent variable model (GP-LVM) is utilized for low-dimensional representation of the original configuration space. Second, an approximate inference algorithm is used, exploiting through the duality between control and estimation, to explore the decision space and to compute a high-quality motion trajectory of the robot. Utilizing the GP-LVM and the duality between control and estimation, we construct a fully probabilistic generative model with which a high-dimensional motion planning problem is transformed into a tractable inference problem. Finally, we compute the motion trajectory via an approximate inference algorithm based on a variant of the particle filter.