Generating a height-map to surface of a cube. Thread

I have been playing around with the diamond-square algorithm to generate six equally sized height-maps that can be placed next to each other to create the illusion that the surface is a cube. The result is shifting back and forth between This-can-be-something! and Minecraft-far-lands. I have come to realise that diamond-square maybe not is suitable when sides are being folded, so now I'm asking here if someone know another algorithm that is more suitable to my goal or if someone actually has got diamond-square to work on a cube.

Next approach I will try out is generating a generic T-shaped height-map and then try to smooth out the sides that are being stitch together in post.

NOTE: I do not intend to generate a cube, it would just look like a cube if you could look at it from far away. The height-map will be used to define land and sea.

EDIT:
I have searched around after a how to apply diamond-square to a cube and found nothing. Then I realised: how do they do it to a sphere then? And as you may have guessed: by createing six squares. Turnsout it's more populate to apply diamond-square to a sphere then to a cube. I wonder why!

EDIT 2:
For future readers: I think I have found a good source: Planet Generator from Københavns Universitet.
In their Planet Map Generator web interface, if you change Projection to Gnomonic and set Width and Height to equal you can rotate Latitude and Longitude by 90 to get each side of the cube.

Edited by: Chris_Acrobat