Procedural Islands Voronoi Pattern

Procedural Islands Voronoi Pattern

I'm trying to keep this as simple as possible, as I've found out the last few days this is a very difficult topic. I'd like to generate multiple flat islands, formed by a voronoi diagram. I've followed a long and (for me) difficult tutorial of building a procedural hexagonal grid just to find out it looks to artificial. 
I'd like to create a plane with faces divided in a voronoi diagram, and extrude multiple groups upwards to create islands. With that I'd like to achieve something similar as this: http://applemagazine.com/wp-content/uploads/2015/10/image2.jpg
Please help to get me started in the right direction, since my approach might be wrong in itself.
EDIT:
I've found this: https://github.com/jceipek/Unity-delaunay. Which draws lines in a voronoi diagram. Now I'm guessing the next step is to convert this to a mesh. Then I'd have to highlight random faces to be extruded to create the islands. Maybe this could be done with perlin noise, which I've just learned about. Extruding might not be the best way. Maybe deleting the faces that won't be land, and creating fall of edges (Like Wardy said).  I'm doing my best to figure this out on my own, but any help is greatly appreciated. 

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