What is the diffuse ionized gas? I've been trying to find a clean definition what people mean by when they talk about diffuse ionized gas in the interstellar medium, but I couldn't find anything so far.
Apparently it's supposed to be trivial.

Is it simply ionized gas, mixed with non-ionized gas in the ISM through the process of diffusion?
The "diffuse ionized gas" (DIG) is another term for the phase of the interstellar medium (ISM) usually called the warm ionized medium (WIM). With a temperature of the order $10^4\,\mathrm{K}$, but extenting to lower and higher temperatures, it is hot enough to keep hydrogen ionized, and various metals exist as low-ionization species, such as S II, N II, and O II, and even (weak) O III (e.g. Hill et al. 2012; Zang et al. 2017; Weilbacher et al. 2018).

Rough pressure equilibrium with the other phases of the ISM results in characteristic densities of $0.1\,\mathrm{cm}^{-1}$, but typical ranges are an order of magnitude to both sides.

A review of the DIG/WNM can be found in Haffner et al. (2009).