i'm on a pretty much exclusively milk/yoghurt based diet. i fart a bit from milk but yoghurt does seem to exclude this. Also, the milk farts were not that bad compared to the potato/sugar/seed oils farst.

carbs make CO2, fats don't. carbs are all synthesised, at base, from ethanol. effectively, all carbs are alcohols, look at all the OH you see on the chemical diagrams.

having said that, the sugar in milk is unique in that almost no bacteria grow off it except the duo of lactobacillis and acidophilus, and the first thing that happens is the sugar is turned into lactic acid. so, no gas is emitted from this fermentation. you just get elimination of carbs and conversion from casein to BCAAs.