We consider the action of the group of Hamiltonian diffeomorphisms on the space of compatible almost complex structures of a symplectic manifold, with the scalar curvature as an equivariant moment map (due to Donaldson and Fujiki). While the Mabuchi K-energy measures 'displacement' transverse to the orbits, we propose a way to measure 'displacement' along an orbit, to obtain a function on the universal cover of the group satisfying the homomorphism property up to a uniformly bounded error - a quasimorphism. This construction agrees with previous results of Ruelle, Barge-Ghys, Entov and Py. Moreover, the same construction works in finite-dimensional settings, giving the (essentially unique) Guichardet-Wigner quasimorphisms on Hermitian Lie groups.