  Let $M_q(H_{\mathbb{R}})$ be the $q$-Gaussian von Neumann algebra associated
with a separable infinite dimensional real Hilbert space $H_{\mathbb{R}}$ where
$-1 < q < 1$. We show that $M_q(H_{\mathbb{R}}) \not \simeq
M_0(H_{\mathbb{R}})$ for $-1 < q \not = 0 < 1$. The C$^\ast$-algebraic
counterpart of this result was obtained recently in [BCKW22]. Using ideas of
Ozawa we show that this non-isomorphism result also holds on the level of von
Neumann algebras.
