  We establish kinetic Hamiltonian flows in density space embedded with the
$L^2$-Wasserstein metric tensor. We derive the Euler-Lagrange equation in
density space, which introduces the associated Hamiltonian flows. We
demonstrate that many classical equations, such as Vlasov equation,
Schr{\"o}dinger equation and Schr{\"o}dinger bridge problem, can be rewritten
as the formalism of Hamiltonian flows in density space.
