  We investigate the relation between thermodynamic and dynamic properties of
an associating lattice gas (ALG) model. The ALG combines a three dimensional
lattice gas with particles interacting through a soft core potential and
orientational degrees of freedom. From the competition between the directional
attractive forces and the soft core potential results two liquid phases, double
criticality and density anomaly. We study the mobility of the molecules in this
model by calculating the diffusion constant at a constant temperature, $D$. We
show that $D$ has a maximum at a density $\rho_{max}$ and a minimum at a
density $\rho_{min}<\rho_{max}$. Between these densities the diffusivity
differs from the one expected for normal liquids. We also show that in the
pressure-temperature phase-diagram the line of extrema in diffusivity is close
to the liquid-liquid critical point and it is partially inside the temperature
of maximum density (TMD) line.
