Diamond compounds are in fact 'lapping pastes' and not really grindings pastes. There primary use is for the finishing of hardened materials, (Hence why its diamond) very commonly used in Toolrooms for press tool and mould work. I believe this is where they derived from and have now become common place to all due to cheap imports and 'sell anything people will buy type policy' from a lot of the cheaper tool import companies, who of course will remain nameless. Although those imports will not be anything like the 'real product'. For all intents and purposes its really a gimmick for the home domestic garage guy/ home machine shop unless you are working with jobs where its actually needed which is pretty doubtful given lapping pastes true purpose. I expect there are whole ton of weird and wonderful products using the term 'Diamond' as a selling point, consider it the same as mens razors being sold with the name 'Turbo' as an advertising phrase, in other words utter rubbish that only a fool will fall for. They are also normally used with a liquid to dilute the compound to form a slurry.
just doing a google search and found one 'Diamond product' for polishing brass and copper etc why in gods name do you need anything as expensive and hard as diamond to polish brass and copper................ Ya dont!............... rest my case!