  In this paper, we obtain new $d$-dimensional and asymptotically flat wormhole
solutions by assuming a specific form of the energy density distribution. This
is addressed by considering the generalization of the so-called Dymnikova
model, originally studied in the context of regular black holes. In this way,
we find constraints for the involved parameters, namely, the throat radius, the
scale associated to the matter distribution, and the spacetime dimension, to
build those wormholes. Following, we study the properties of the obtained
solutions, namely, embedding diagrams as well as Weak and Null Energy
Conditions (WEC and NEC). We show that the larger the dimension, the larger the
flatness of the wormhole and the more pronounced the violation of these energy
conditions. We also show that the corresponding fluid behaves as phantom-like
for $d \geq 4$ in the neighborhood of the wormhole throat. In addition, we
specialize the employed model for $d=4$ spacetime, associating it with the
gravitational analog of the Schwinger effect in a vacuum and correcting the
model by introducing a minimal length via Generalized Uncertainty Principle
(GUP). Thus, we obtain a novel traversable and asymptotically flat wormhole
solution by considering that the minimal length is very tiny. The associated
embedding diagram shows us that the presence of this fundamental quantity
increases the slope of the wormhole towards its throat compared with the case
without it. That correction also attenuates the WEC (and NEC) violations nearby
the throat, with the fluid ceasing to be a phantom-type at the Planck scale,
unlike the case without the minimal length.
