  Context. Multiple mechanisms are known to give rise to turbulence in
protoplanetary disks, which facilitates the accretion onto the central star.
Small dust particles that are well coupled to the gas undergo diffusion due to
this turbulent motion. Aims. This paper investigates the influence of
turbulence induced dust diffusion on the equilibrium of protoplanetary disks.
Methods. The model accounts for dust sublimation, radiative transfer with the
flux-limited diffusion approximation and dust diffusion. It predicts the
density and temperature profiles as well as the dust-to-gas ratio of the disk.
Results. It is shown that dust diffusion can have a large impact: assuming the
dust survives for 104 seconds or longer before it can be evaporated, leads the
dust diffusion to widen the inner disk considerably. The latter effect is
generated through a feedback mechanism as the diffusion length is much smaller
than the disk width. With increasing dust diffusion, the inclination of the
inner rim towards the stellar radiation becomes steeper until it is almost
vertical. The temperature range of evaporation and condensation, which is
linked to the dust composition, has no influence on this effect. Conclusions.
For realistic parameters dust diffusion can not be neglected when determining
the equilibrium of the disk. Stronger turbulence inside the disk induces more
dust diffusion. Therefore, the dust density grows more gradually over a greater
distance and less radiation reaches the disk surface. The new equilibrium shape
of the disk is more inclined towards the star. This effect is universal and
independent of the specific dust composition.
