In this paper, we investigate an off-line strategy to incorporate inter-fraction organ motion in IMRT treatment planning. It was suggested that inverse planning could be based on a probability distribution of patient geometries instead of a single snap shot. However, this concept is connected to two intrinsic problems: first, this probability distribution has to be estimated from only a few images; and second, the distribution is only sparsely sampled over the treatment course due to a finite number of fractions. In the current work, we develop new concepts of inverse planning which account for these two problems.