  We establish weak existence and uniqueness in law for stochastic Volterra
equations (SVEs for short) with completely monotone kernels and non-degenerate
noise under mild regularity assumptions. In particular, our results reveal the
regularization-by-noise effect for SVEs with singular kernels, allowing for
multiplicative noise with H\"{o}lder diffusion coefficients. In order to prove
our results, we reformulate the SVE into an equivalent stochastic evolution
equation (SEE for short) defined on a Gelfand triplet of Hilbert spaces. We
prove weak well-posedness of the SEE using stochastic control arguments, and
then translate it into the original SVE.
