A more thorough geochemical description is provided in the article Kimberlite ascent by assimilation-fuelled buoyancy (Russell et al. 2012), the proposed model mechanism as the original kimberlite melt to be carbonatite-like - poor in silica content, this magma assimilates materials during its accent through the upper mantle and crust, becoming more silicic, causing the $\mathrm{CO}_2$ solubility to decrease, reducing density and increasing buoyancy, causing the magma to accelerate.

In terms of why cratonic crust is the locale of many diamond rich kimberlite pipes is described from Professor Dingwell as being due to the silica rich cratonic crust is thick enough to provide the magma to make contact with the silicate rich minerals therein.