First, there is a difference between fat loss/gain and weight loss/gain. So if you are on a very low carb diet and you start eating carbs you will gain weight as your body increases it's glycogen stores. For a large person this can represent 5 lbs or more. (For me it's about 8 lbs) This is not a gain in fat. Dispite what the IP diet says about insulin and ketosis fat loss/gain is always going to be an equation of energy/calories.
Second, when you're on a very low calorie diet, like IP, eating more food means you have more digesting and greater waste. Again, depending on the size of the person this can be 2-4 lbs. Also a gain in weight only, not fat.
Third, if you fall off the wagon and start eating you're very likely going to increase your sodium intake massively which results in more water retention. Nothing to do with fat gain. Some people this can be a very large contributor to weight gain.
As for actual fat gain - it is a matter of calories.
"Getting solid information is easier than ever. Getting misinformation is even easier." - Kaplods
Maintaining for two years and I eat whatever I want - just not however much I want. Details here.