We examine the radial distributions of stellar populations in the globular cluster (GC) M15, using Hubble Space Telescope/Wide Field Camera 3 (WFC3) photometry of red giants in the nitrogen-sensitive F343N-F555W color. Surprisingly, we find that giants with "primordial" composition (i.e., N abundances similar to those in field stars) are the most centrally concentrated within the WFC3 field. We then combine our WFC3 data with Sloan Digital Sky Survey u,g photometry and find that the trend reverses for radii >~1' (3pc) where the ratio of primordial to N-enhanced giants increases outward, as already found by Lardo et al. (2011A&A...525A.114L). The ratio of primordial to enriched stars thus has a U-shaped dependency on radius with a minimum near the half-light radius. N-body simulations show that mass segregation might produce a trend resembling the observed one, but only if the N-enhanced giants are ~0.25M_{sun}_ less massive than the primordial giants, which requires extreme He enhancement (Y>~0.40). However, such a large difference in Y is incompatible with the negligible optical color differences between primordial and enriched giants, which suggest {Delta}Y<~0.03 and thus a difference in turn-off mass of {Delta}M<~0.04M_{sun}_ between the different populations. The radial trends in M15 are thus unlikely to be of dynamical origin and presumably reflect initial conditions, a result that challenges all current GC formation scenarios. We note that population gradients in the central regions of GCs remain poorly investigated and may show a more diverse behavior than hitherto thought.