In this paper we consider diffusion semigroups generated by second order differential
operators of degenerate type. The operators that we consider do not, in general, satisfy the
H¨ormander condition and are not hypoelliptic. In particular, instead of working under the H¨ormander
paradigm, we consider the so-called UFG condition, introduced by Kusuoka and Strook in the
eighties. The UFG condition is weaker than the uniform H¨ormander condition, the smoothing effect
taking place only in certain directions (rather than in every direction, as it is the case when the
H¨ormander condition is assumed). Under the UFG condition, Kusuoka and Strook deduced sharp
small time asymptotic bounds for the derivatives of the semigroup in the directions where smoothing
occurs. In this paper, we study the large time asymptotics for the gradients of the diffusion
semigroup in the same set of directions and under the same UFG condition. In particular, we identify
conditions under which the derivatives of the diffusion semigroup in the smoothing directions
decay exponentially in time. This paper constitutes therefore a stepping stone in the analysis of
the long time behaviour of diffusions which do not satisfy the H¨ormander condition