  We study the smooth $2$-group structure arising in the presence of quantum
field theory with one-form symmetry. We acquire $2$-group structures obtained
by a central extension of the zero-form symmetry by the one-form symmetry. We
determine that the existence of a $2$-group structure is guaranteed by
Chern--Simons levels. We further verify how we will be able to provide a fix to
the current $2$-group problems by using the bibundle model. We outline the
principal $2$-connection theory with respect to such $2$-group and compare it
with the ansatz obtained from the Green--Schwarz mechanism. We further propose
the existence of smooth $\infty$-group symmetries in quantum field theory.
