Technically, the diamond dust is in the flame. By the time it leaves the flame, it's been broken down to CO2. What you see in this picture is actually wax vapor, which is the fuel that actually burns in a candle. The wick is just there to heat the wax to the point of vaporizing, because solid/liquid wax does not burn. This is why you can light the smoke trail coming off of a snuffed out candle to re-light it.

Funnily enough, that gif also came from /r/woahdude.

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