Hi glmr.

Well...I first chamfered in Moi the edges of the Voronoi walls, as you can see here




Then I exported in obj format and finally loaded in 3D-Coat.
There I have voxelized the imported object and applied a Shader.
Last stage, the render with 3D-Coat's Render Room using its builtin PBR renderer.

I often use this "trick" to create "quick and dirt" rendering with super smooth edges without the need to do the "fillet" stage in Moi.
Using 3D-Coat's Voxels I can get super-exaggerated smooth edges in the blink of an eye.
But in this case you need to create Voxels with very high poly count, many millions, and you need a decent CPU+GPU to do that.

But if you have time to spent and want to do the things with better precision then I'm pretty sure that you can fillet the Voronoi walls directly in Moi.

Anyway...this is just one of many ways to get "smooth" edges on Voronoi structures.

3D-Coa's way is one of my preferred, but only because it fits perfectly in one of my wokflows for "2D/3D image composition".
Quick and easy.

But it's a very personal technique, maybe others can find it too "coarse".

Ciao!