Off the top of my head each individual face of your cube is tessellated and then displaced.
You need to ensure that the edge vertices are shared in each (subdivided) side-face or else these seams will occur since all vertices on the top face are displaced only along the up axis and all vertices of the front face are displaced only along the depth axis.
A simple solution is to displace along the vertex normals and ensure that whereever you have overlapping vertices (such as at the corners of a cube) you set the normal of all such vertices to the average of all "actual" vertex normals at that position. This will make the edges a bit more bulky but keep the faces connected.
My previous post in this thread (just above yours) describes how I solved this in a relatively simple way in more detail.