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Centrifuge experiments on olivine, chromite, and plagioclase aggregates saturated in basaltic liquid show evidence of viscous compaction by grain‐boundary diffusion‐controlled creep. The experiments confirm that the exponential dependence of shear viscosity on melt fraction, observed at low porosities in earlier shear deformation experiments, extends to sedimentary porosities. The compaction profiles are inconsistent with the porosity‐dependence commonly ascribed to viscosity in macroscopic compaction models, which underestimate the effect of matrix disaggregation and consequently overestimate the viscosities of crystal mushes by 1–2 orders of magnitude. The time to halve the porosity of natural olivine igneous sediments by compaction is estimated from the centrifuge experiments to be O(103)y. Half‐times for plagioclase and chromite layers are O(104–105)y, suggesting that such layers compact on magmatic time scales only if they are loaded by additional sedimentation. At conditions relevant to melt flow in asthenospheric settings and trans‐crustal magmatic systems, the bulk and shear viscosities inferred for olivine and plagioclase are O(1017)Pa s, 4 orders of magnitude less than inferred from earlier experimental studies of the diffusion creep rheology. The reduced viscosities imply time‐ and length‐scales for compaction processes that are substantially shorter than previously anticipated. Our analysis serendipitously reveals that the oft‐neglected solidity term of the Carman‐Kozeny porosity‐permeability relation is essential to prevent non‐physical behavior in models of cumulate compaction. Plain Language Summary: The weight of the rocks overlying partially molten regions of the Earth squeezes melt toward the surface. This process is usually limited by rock viscosity and because rock viscosities are extremely high it is not easily observed. We review three sets of experiments on common crustal and mantle minerals in which melt expulsion was accelerated in a centrifuge. The results are consistent with recent theoretical models for rock viscosity and suggest that melt expulsion is substantially faster than previously anticipated. Key Points: Experimental compaction profiles are consistent with a porosity‐weakening effect predicted for grain‐boundary controlled diffusion creepBulk viscosities for plagioclase and olivine aggregates are three orders of magnitude lower than reported from earlier experimentsExtrapolation to natural conditions indicates diffusion creep remains an efficient deformation mechanism in partially molten natural rocks [ABSTRACT FROM AUTHOR]