  A framework for an improved TMD (iTMD) factorization scheme at small $x$,
involving off-shell perturbative subamplitudes, was recently developed as an
interpolation between the TMD $k_t \ll Q$ regime and the BFKL $k_t \sim Q$
regime. In this article, we study the relation between CGC and iTMD amplitudes.
We first show how the dipole-size expansion of CGC amplitudes resembles the
twist expansion of a TMD amplitude. Then, by isolating kinematic twists, we
prove that iTMD amplitudes are obtained with infinite kinematic twist accuracy
by simply getting rid of all genuine twist contributions in a CGC amplitude.
Finally we compare the amplitudes obtained via a proper kinematic twist
expansion to those obtained via a more standard dilute expansion to show the
relation between the iTMD framework and the dilute low $x$ framework.
