  We provide an entropy formulation for porous medium-type equations with a
stochastic, non-linear, spatially inhomogeneous forcing. Well - posedness and
$L_1$-contraction is obtained in the class of entropy solutions. Our scope
allows for porous medium operators $\Delta (|u|^{m-1}u)$ for all
$m\in(1,\infty)$, and H\"older continuous diffusion nonlinearity with exponent
$1/2$.
