  Cosmic strings are linear topological defects that may have been produced
during symmetry-breaking phase transitions in the very early Universe. In an
expanding Universe the existence of causally separate regions prevents such
symmetries from being broken uniformly, with a network of cosmic string
inevitably forming as a result. To faithfully generate observables of such
processes requires computationally expensive numerical simulations, which
prohibits many types of analyses. We propose a technique to instead rapidly
emulate observables, thus circumventing simulation. Emulation is a form of
generative modelling, often built upon a machine learning backbone. End-to-end
emulation often fails due to high dimensionality and insufficient training
data. Consequently, it is common to instead emulate a latent representation
from which observables may readily be synthesised. Wavelet phase harmonics are
an excellent latent representations for cosmological fields, both as a summary
statistic and for emulation, since they do not require training and are highly
sensitive to non-Gaussian information. Leveraging wavelet phase harmonics as a
latent representation, we develop techniques to emulate string induced CMB
anisotropies over a 7.2 degree field of view, with sub-arcminute resolution, in
under a minute on a single GPU. Beyond generating high fidelity emulations, we
provide a technique to ensure these observables are distributed correctly,
providing a more representative ensemble of samples. The statistics of our
emulations are commensurate with those calculated on comprehensive Nambu-Goto
simulations. Our findings indicate these fast emulation approaches may be
suitable for wide use in, e.g., simulation based inference pipelines. We make
our code available to the community so that researchers may rapidly emulate
cosmic string induced CMB anisotropies for their own analysis.
