1. A medical image display apparatus, comprising: a diagnostic image displaying unit configured to display a diagnostic image generated by voxel values in a predefined range formed along a predefined direction in volume data based on a slice image group; a range dividing unit configured to divide a range after changing into (1) an overlapping range in which the range after changing overlaps a range before changing, and (2) a non-overlapping range that does not include the overlapping range, when a position of the range before changing is changed in the predefined direction; a pixel value after changing setting unit configured to set a pixel value after changing (1) based on a pixel value constituting a diagnostic image before changing and voxel values along the predefined direction in the non-overlapping range according to a predefined condition when a position of a voxel value in the volume data corresponding to the pixel value constituting the diagnostic image before changing exists in the overlapping range, and (2) based on voxel values along the predefined direction in the range after changing according to the predefined condition when the position does not exist in the overlapping range, for each pixel constituting a diagnostic image after changing generated based on the voxel values along the predefined direction in the range after changing; and a diagnostic image generating unit configured to generate the diagnostic image after changing based on each pixel value after changing set by the pixel value after changing setting unit.