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In this paper, we study diffeological spaces as certain kinds of discretesimplicial presheaves on the site of cartesian spaces with the coverage of goodopen covers. The \v{C}ech model structure on simplicial presheaves provides uswith a notion of $\infty$-stack cohomology of a diffeological space with valuesin a diffeological abelian group $A$. We compare $\infty$-stack cohomology ofdiffeological spaces with two existing notions of \v{C}ech cohomology fordiffeological spaces in the literature. Finally, we prove that for adiffeological group $G$, that the nerve of the category of diffeologicalprincipal $G$-bundles is weak homotopy equivalent to the nerve of the categoryof $G$-principal $\infty$-bundles on $X$, bridging the bundle theory ofdiffeology and higher topos theory.

Diffeological Principal Bundles and Principal Infinity Bundles