  Let $P$ be a closed convex cone in $\mathbb{R}^{d}$ which we assume to be
spanning and pointed i.e. $P-P=\mathbb{R}^{d}$ and $P \cap -P=\{0\}$. In this
article, we consider CCR flows over $P$ associated to isometric representations
that arises out of $P$-invariant closed subsets, also called as $P$-modules, of
$\mathbb{R}^{d}$. We show that for two $P$-modules the associated CCR flows are
cocycle conjugate if and only if the modules are translates of each other.
