  First essential m-dissipativity of an infinite-dimensional Ornstein-Uhlenbeck
operator $N$, perturbed by the gradient of a potential, on a domain
$\mathcal{F}C_b^{\infty}$ of finitely based, smooth and bounded functions, is
shown. Our considerations allow unbounded diffusion operators as coefficients.
We derive corresponding second order regularity estimates for solutions $f$ of
the Kolmogorov equation $\alpha f-Nf=g$, $\alpha \in (0,\infty)$, generalizing
some results of Da Prato and Lunardi. Second we prove essential m-dissipativity
for generators $(L_{\Phi},\mathcal{F}C_b^{\infty})$ of infinite-dimensional
non-linear degenerate diffusion processes. We emphasize that the essential
m-dissipativity of $(L_{\Phi},\mathcal{F}C_b^{\infty})$ is useful to apply
general resolvent methods developed by Beznea, Boboc and R\"ockner, in order to
construct martingale/weak solutions to infinite-dimensional non-linear
degenerate diffusion equations. Furthermore, the essential m-dissipativity of
$(L_{\Phi},\mathcal{F}C_b^{\infty})$ and $(N,\mathcal{F}C_b^{\infty})$, as well
as the regularity estimates are essential to apply the general abstract Hilbert
space hypocoercivity method from Dolbeault, Mouhot, Schmeiser and Grothaus,
Stilgenbauer, respectively, to the corresponding diffusions.
