3d Perlin Noise used to generate terrain, but it's not voxel. IT'S MADE OF VERTICES AND A CUSTOM MESH.

So I get the general idea for using 3d perlin noise for terrain generation. But this terrain will have overhangs and caves. I know that I have to treat the data from the 3d perlin noise as density. I get all of that. But most examples use cubes to show the terrain. That's cool and all, but I would like to have a more realistic terrain. So I thought if people create custom meshes for terrain generation using 2d perlin noise, then maybe it should be possible to create custom meshes for terrain generation using 3d perlin noise. I guess you can replace the cubes with the vertices, but then you would have to connect the vertices with planes (triangles and squares), so that it isn't hollow. The thing is, I don't know how to make the vertices to begin with. AND, I don't know how to make the planes that'll connect the points. So my progress has halted. Any advice? Any tips? Any answers? Any suggestions? Thank you in advance!