  This article is accepted for publication in the "Annals I.H.P. Prob. &
Stat.". We investigate the ballistic behavior of diffusions in random
environment. We introduce conditions in the spirit of (T) and (T') of the
discrete setting, cf. Sznitman \cite{szn01}, \cite{szn02}, that imply in higher
dimensions a strong law of large numbers with non-vanishing limiting velocity
(which we refer to as 'ballistic behavior') and a functional central limit
theorem with non-degenerate covariance matrix. As an application of our
results, we consider the class of diffusions where the diffusion matrix is the
identity, and give a concrete criterion on the drift term under which the
diffusion in random environment exhibits ballistic behavior. This criterion
provides new examples of ballistic diffusions in random environment.
