NNLO+PS predictions for Higgs production through bottom-quark fusion

We present next-to-next-to-leading-order (NNLO) QCD corrections for Higgs production through bottom-quark annihilation ($b\bar{b}H$) matched to parton showers (NNLO+PS) using the MiNNLO$_{\rm PS}$ technique. The MiNNLO$_{\rm PS}$ method is adapted for the extra scale dependence due to the Yukawa coupling renormalized in the $\overline{\rm MS}$ scheme. The computation has been carried out in the five flavour scheme (5FS) neglecting the bottom mass. Results are compared against fixed-order predictions at NNLO and resummed predictions at next-to-next-to-leading-logarithmic (NNLL) accuracy. We also present preliminary results within the four-flavour scheme (4FS) setup, reaching a new level of precision in the massive scheme.