There exists an elementary result in the Malliavin calculus that for the considered SDE, provided all derivatives of the drift are bounded, the corresponding measure becomes infinite times differentiable. I was wondering if there is a less restrictive yet sufficient condition for smoothness of the measure (and hence the transition probability density). For example, I can imagine Novikov's condition and therefore using the Girsanov transformation may lead to a smoothness result for the measure; without actually requiring derivatives of the drift to be bounded. I really appreciate if someone shares his/her ideas about the question.