  We prove existence of weak solutions for a diffuse interface model for the
flow of two viscous incompressible Newtonian fluids with different densities in
a bounded domain in two and three space dimensions. In contrast to previous
works, we study a model with a singular non-local free energy, which controls
the $H^{\alpha/2}$-norm of the volume fraction. We show existence of weak
solutions for large times with the aid of an implicit time discretization.
