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In this paper, we explore the version of Hairer's regularity structures basedon a greedier index set than trees, as introduced by Otto, Sauer, Smith andWeber. More precisely, we construct and stochastically estimate therenormalized model avoiding the use of Feynman diagrams but still in a fullyautomated, i. e. inductive way. This is carried out for a class of quasi-linearparabolic PDEs driven by noise in the full singular but renormalizable range.We assume a spectral gap inequality on the (not necessarily Gaussian) noiseensemble. The resulting control on the variance of the model naturallycomplements its vanishing expectation arising from the BPHZ-choice ofrenormalization. We capture the gain in regularity on the level of theMalliavin derivative of the model by describing it as a modelled distribution.Symmetry is an important guiding principle and built-in on the level of therenormalization Ansatz. Our approach is analytic and top-down rather thancombinatorial and bottom-up.

A diagram-free approach to the stochastic estimates in regularity structures