  We present a complementary methodology to constrain the total neutrino mass,
$\sum m_{\nu}$, based on the diffusion coefficient of the splashback mass
function of dark matter halos. Analyzing the snapshot data from the Massive
Neutrino Simulations, we numerically obtain the number densities of distinct
halos identified via the SPARTA code as a function of their splashback masses
at various redshifts for two different cases of $\sum m_{\nu}=0.0$ eV and $0.1$
eV. Then, we fit the numerical results to the recently developed analytic
formula characterized by the diffusion coefficient that quantifies the degree
of ambiguity in the identification of the splashback boundaries. Our analysis
confirms that the analytic formula works excellently even in the presence of
neutrinos and that the decrement of its diffusion coefficient with redshift is
well described by a linear fit, $B(z-z_{c})$, in the redshift range of $0.2\le
z\le 2$. It turns out that the massive neutrino case yields significantly lower
value of $B$ and substantially higher value of $z_{c}$ than the massless
neutrino case, which indicates that the higher masses the neutrinos have, the
more severely the splashback boundaries become disturbed by the surroundings.
Given our result, we conclude that the total neutrino mass can in principle be
constrained by measuring how rapidly the diffusion coefficient of the
splashback mass function diminishes with redshifts at $z\ge 0.2$. We also
discuss the anomalous behavior of the diffusion coefficient found at lower
redshifts for both of the $\sum m_{\nu}$ cases, and ascribe it to the
fundamental limitation of the SPARTA code at $z\le 0.13$.
