Connection on the group of diffeomorphisms as a bundle over the space of functions

Jacobian determines a bundle with total space consisting of orientation-preserving diffeomorphisms of a (connected) manifold over the space of positive functions on this manifold (with integral equal to volume for a compact manifold). It is proved that, for the $n$-sphere with standard metric, there is a unique connection on this bundle that is invariant with respect to all isometries of the sphere, and a description of this connection is given.