That is a good question. I'm not aware of someone exploring this avenue, but it would be interesting to see what categories of models are fooled by what types of noise.
"Noise" is the wrong way to think about these IMO, while robustness to noise implies robustness to a degree of perturbations, the perturbations have clearly outlined "directions" which can be visualised via so called "church plots". Seyed-Mohsen Moosavi-Dezfooli http://smoosavi.me/ and the lab of Prof. Frossard have done amazing work exploring this.
