  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 $z\sim2.5$. 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 $z\sim2$. 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 $r\sim5$ 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.
