Experimental, theoretical, and numerical results are presented for the dynamics of interacting and deforming diapirs. The clustering of diapirs may occur as a result of the deformation induced by their mutual interactions. The time required for two diapirs in the mantle to merge can be small compared to their ascent time. The clustering of many diapirs, however, is a relatively slow process and is unlikely to significantly affect their distribution in the Earth's mantle. If coronae on Venus are produced by diapirs, diapir clustering may explain the variation of coronae size, and may be related to the observed clustering of coronae on the surface.