  We present two different arguments using stochastic analysis to construct
super-renormalizable tensor field theories, namely the $\mathrm{T}^4_3$ and
$\mathrm{T}^4_4$ models. The first approach is the construction of a Langevin
dynamic combined with a PDE energy estimate while the second is an application
of the variational approach of Barashkov and Gubinelli. By leveraging the
melonic structure of divergences, regularising properties of non-local
products, and controlling certain random operators, we demonstrate that for
tensor field theories these arguments can be significantly simplified in
comparison to what is required for $\Phi^4_d$ models.
