We present spatially-resolved Atacama Large Millimeter/sub-millimeter Array (ALMA) 870 $mu$m dust continuum maps of six massive, compact, dusty star-forming galaxies (SFGs) at $zsim2.5$. These galaxies are selected for their small rest-frame optical sizes ($r_{rm e, F160W}sim1.6$ kpc) and high stellar-mass densities that suggest that they are direct progenitors of compact quiescent galaxies at $zsim2$. The deep observations yield high far-infrared (FIR) luminosities of L$_{rm IR}=10^{12.3-12.8}$ L$_{odot}$ and star formation rates (SFRs) of SFR$=200-700$ M$_{odot}$yr$^{-1}$, consistent with those of typical star-forming main sequence galaxies. The high-spatial resolution (FWHM$sim$0.12-0.18) ALMA and HST photometry are combined to construct deconvolved, mean radial profiles of their stellar mass and (UV+IR) SFR. We find that the dusty, nuclear IR-SFR overwhelmingly dominates the bolometric SFR up to $rsim5$ kpc, by a factor of over 100$times$ from the unobscured UV-SFR. Furthermore, the effective radius of the mean SFR profile ($r_{rm e, SFR}sim1$ kpc) is $sim$30% smaller than that of the stellar mass profile. The implied structural evolution, if such nuclear starburst last for the estimated gas depletion time of $Delta t=pm100$ Myr, is a 4$times$ increase of the stellar mass density within the central 1 kpc and a 1.6$times$ decrease of the half-mass radius. This structural evolution fully supports dissipation-driven, formation scenarios in which strong nuclear starbursts transform larger, star-forming progenitors into compact quiescent galaxies.
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