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CaMgSi2O6 and CaSiO3 liquids have been investigated over the entire mantle pressure regime using first principles molecular dynamics simulations with density functional theory in the local density approximation and the ultra-soft plane-wave pseudopotential method. The equilibrated liquid structure is much more densely packed at high pressure. The average Si-O coordination number increases nearly linearly from 4 to 6 with compression. The results are well fitted by Mie-Grüneisen equation of state, , with a Grüneisen parameter that linearly increases and heat capacity that linearly decreases with compression. The total and self diffusion coefficients of diopside liquid exhibit an unusual pressure dependence, first decreasing with increasing pressure, than increasing, and finally decreasing again at the highest pressures. This pattern is explained by the pressure-induced decrease in the number of excess non-bridging oxygens at low pressure, and the increase in the number of 5-fold coordinated silicons at higher pressures. Mg has a slightly higher self-diffusion coefficient than Ca, both of which are slightly more diffusive than O and Si. The average activation energy over the temperature range 3000-6000 K is lower than that found experimentally at lower temperatures, consistent with non-Arrhenian behavior. We combine our results with previous results on MgSiO3 composition to determine the volume of mixing on the MgSiO3-CaSiO3 join. The volume of mixing is zero within uncertainty.