  We establish the large scale convergence of a class of stochastic weakly
nonlinear reaction-diffusion models on a three dimensional periodic domain to
the dynamic $\Phi^4_3$ model within the framework of paracontrolled
distributions. Our work extends previous results of Hairer and Xu to
nonlinearities with a finite amount of smoothness (in particular $C^9$ is
enough). We use the Malliavin calculus to perform a partial chaos expansion of
the stochastic terms and control their $L^p$ norms in terms of the graphs of
the standard $\Phi^4_3$ stochastic terms.
