From the book "Heat Kernels and Dirac Operators" (Getzler et al):
Recall that the bundle $|\Lambda|^s$ of $s$-densities on a Riemannian manifold has a natural connection, which preserves the canonical section $|dx|^s$
Unfortunately Getzler does not provide any reference and I don't even know what "preserves" means in this context. Can someone please elaborate?