A generalized metric on a manifold
M
M
, i.e., a pair
(
g
,
H
)
(g,H)
, where
g
g
is a Riemannian metric and
H
H
a closed
3
3
-form, is a fixed point of the generalized Ricci flow if and only if
(
g
,
H
)
(g,H)
is Bismut Ricci flat:
H
H
is
g
g
-harmonic and
R
c
(
g
)
=
1
4
H
g
2
Rc(g)=\tfrac {1}{4}H_g^2
. On any homogeneous space
M
=
G
/
K
M=G/K
, where
G
=
G
1
×
G
2
G=G_1\times G_2
is a compact semisimple Lie group with two simple factors, under some mild assumptions, we exhibit a Bismut Ricci flat
G
G
-invariant generalized metric, which is proved to be unique among a
4
4
-parameter space of metrics in many cases, including when
K
K
is neither abelian nor semisimple. On the other hand, if
K
K
is simple and the standard metric is Einstein on both
G
1
/
π
1
(
K
)
G_1/\pi _1(K)
and
G
2
/
π
2
(
K
)
G_2/\pi _2(K)
, we give a one-parameter family of Bismut Ricci flat
G
G
-invariant generalized metrics on
G
/
K
G/K
and show that it is most likely pairwise non-homothetic by computing the ratio of Ricci eigenvalues. This is proved to be the case for every space of the form
M
=
G
×
G
/
Δ
K
M=G\times G/\Delta K
and for
M
35
=
S
O
(
8
)
×
S
O
(
7
)
/
G
2
M^{35}=SO(8)\times SO(7)/G_2
.