Diamond is not the stable carbon allotrope at low pressure, so if you perform a purely thermal low-pressure method, you will end up with some form of sp2 carbon (graphene, graphite, CNTs).
Therefore, CVD growth of diamond also only works by plasma enhancement in which mainly the hydrogen constantly etches away everything that's graphitic. Plasma-enhanced MBE also exists, but I am not aware of anyone successfully doing that so far for diamond.