  We study the evolution of a system composed by a 1.4 \msun neutron star and a
normal, solar composition star of 2 \msun in orbit with a period of 1 day.
Calculations were performed employing the binary hydro code presented in
Benvenuto & De Vito (2003) that handle the mass transfer rate in a fully
implicit way. Now we included the main standard physical ingredients together
with diffusion processes and a proper outer boundary condition. We have assumed
fully non - conservative mass transfer episodes.
  In order to study the interplay of mass loss episodes and diffusion we
considered evolutionary sequences with and without diffusion in which all Roche
lobe overflows (RLOFs) produce mass transfer. Another two sequences in which
thermonuclearly-driven RLOFs are not allowed to drive mass transfer have been
computed with and without diffusion. To our notice, this study represents the
first binary evolution calculations in which diffusion is considered.
  The system produces a helium white dwarf of \sim 0.21 \msun in an orbit with
a period of \sim 4.3 days for the four cases. We find that mass transfer
episodes induced by hydrogen thermonuclear flashes drive a tiny amount of mass
transfer. As diffusion produces stronger flashes, the amount of hydrogen - rich
matter transferred is slightly higher than in models without diffusion.
  We find that diffusion is the main agent in determining the evolutionary
timescale of low mass white dwarfs even in presence of mass transfer episodes.
