Generalized $q$-Gaussian von Neumann algebras with coefficients, II. Absence of central sequences

We show that the generalized $q$-gaussian von Neumann algebras with coefficients ${\mathrm{\Gamma }}_q(B,S\otimes H)$ with $B$ a finite dimensional factor, dim$(D_k(S))$ sub-exponential and the dimension of $H$ finite and larger than a constant depending on $q$, have no non-trivial central sequences.