  We introduce $L^{2}$-Wasserstein distances on densities of tracial
$W^{*}$-algebras based on a Benamou-Brenier formulation, replacing
multiplication by densities with multiplication operators arising as the
logarithmic mean under a functional calculus. Furthermore, we concern ourselves
with $L^{2}$-Wasserstein distances induced by decomposed derivations on
$C^{*}$-algebras of continuous sections of a $\mathcal{K}(H)$-bundle vanishing
at infinity. We prove a distintegration theorem for such distances, introduce
mean entropic curvature bounds in case $H$ is finite-dimensional and show
control of these by the essential infimum of the entropic curvature bounds on
the fibres. To conclude, we give sufficient conditions for disintegrating
arbitrary $L^{2}$-Wasserstein distances for unital $C^{*}$-algebras that are
Morita equivalent to a commutative unital $C^{*}$-algebra.
