Diamonds made from carbon dioxide might have some value, though as @stanleybmanly wrote, the supply of low cost diamonds would make them as desirable as glass for jewelry. However, it would be valuable for industrial use. And as @dabbler said, the cost to convert CO2 to diamonds in terms of environmental and monetary costs would be prohibitive. Then there is the problem of how much CO2 would be necessary for a given weight of a diamond or a quantity of diamond dust. My guess is that the amount of carbon dioxide converted to pure carbon (which would later be compressed into diamonds) would be negligible.
My fantasy is to convert carbon dioxide and methane (CO2+CH4) into two parts carbon and two parts water (H20). Because carbon has double-valance bonds with oxygen, considerable energy is required to break them (possibly in the form of electromagnetism/photon with a wavelength proportionate to the distance between the carbon and oxygen atoms). However, as hydrogen bonds with oxygen energy is released that may be used to attack the carbon bonds.