  The exact renormalization group (ERG) is a powerful tool for understanding
the formal properties of field theories. By adapting generalized ERG schemes to
the flow of wavefunctionals, we obtain a large class of continuous unitary
networks, a special case of which includes a class of Gaussian continuous
Multi-scale Renormalization Ansatzes (cMERAs). The novel feature of these
generalized wavefunctional ERG schemes is allowing for modifications of the
dispersion relation, which drastically changes the entanglement structure of
the ultraviolet states. Through our construction, we demonstrate that cMERA can
be derived from a more fundamental "microscopic" principle, which amounts to
the usual RG principle of path integral independence, suitably adapted to
quantum states of the field theory. The establishment of such a principle may
provide a path forward for exploring cMERA beyond the free field regime, and
for understanding the nature of entanglement renormalization intrinsically in
the continuum.
