  We analyze circular velocity profiles of seven ultradiffuse galaxies (UDGs)
that are isolated and gas-rich. Assuming that the dark matter halos of these
UDGs have a Navarro-Frenk-White (NFW) density profile or a Read density profile
(which allows for constant-density cores), the inferred halo concentrations are
systematically lower than the cosmological median, even as low as $-0.6$ dex
(about $5\sigma$ away) in some cases. Alternatively, similar fits can be
obtained with a density profile that scales roughly as $1/r^2$ for radii larger
than a few kiloparsecs. Both solutions require the radius where the halo
circular velocity peaks ($R_{\rm max}$) to be much larger than the median
expectation. Surprisingly, we find an overabundance of such large-$R_{\rm max}$
halos in the IllustrisTNG dark-matter-only simulations compared to the Gaussian
expectation. These halos form late and have higher spins compared to median
halos of similar masses. The inner densities of the most extreme among these
late-forming halos are higher than their NFW counterparts, leading to a $\sim
1/r^2$ density profile. However, the two well-resolved UDGs in our sample
strongly prefer lower dark matter densities in the center than the simulated
ones. Comparing to IllustrisTNG hydrodynamical simulations, we also find a
tension in getting both low enough circular velocities and high enough halo
mass to accommodate the measurements. Our results indicate that the gas-rich
UDGs present a significant challenge for galaxy formation models.
