  Difference balanced functions from $F_{q^n}^*$ to $F_q$ are closely related
to combinatorial designs and naturally define $p$-ary sequences with the ideal
two-level autocorrelation. In the literature, all existing such functions are
associated with the $d$-homogeneous property, and it was conjectured by Gong
and Song that difference balanced functions must be $d$-homogeneous. First we
characterize difference balanced functions by generalized difference sets with
respect to two exceptional subgroups. We then derive several necessary and
sufficient conditions for $d$-homogeneous difference balanced functions. In
particular, we reveal an unexpected equivalence between the $d$-homogeneous
property and multipliers of generalized difference sets. By determining these
multipliers, we prove the Gong-Song conjecture for $q$ prime. Furthermore, we
show that every difference balanced function must be balanced or an affine
shift of a balanced function.
