  The notion of a formally smooth bimodule is introduced and its basic
properties are analyzed. In particular it is proven that a $B$-$A$ bimodule $M$
which is a generator left $B$-module is formally smooth if and only if the
$M$-Hochschild dimension of $B$ is at most one. It is also shown that modules
$M$ which are generators in the category $\sigma[M]$ of $M$-subgenerated
modules provide natural examples of formally smooth bimodules.
