Given that the weight gain was based on diet and exercise, but there is no change in exercise -- is there any way to project the rate of weight loss based on diet alone? Meaning the level of exercise/activity would remain the same for the duration of the weight realignment.
There is currently no way to accurately estimate weight loss based on caloric intake. The 3500 calorie deficit = 1 lbs of weight loss idea is appealing, but it is a myth. It does not take into account that foods have different satiety and hormonal responses. Beyond that, the body releases hormones to try to keep you near your current weight.
The ATOZ study compared 4 very popular diets. As is very common with diets, weight loss began well, but plateaued at around 6 months before rebounding. As weight-loss stalled, people actually reduced calories further in order to try to start losing weight again to no avail.
A back of the envelope calculation for these people shows that they were in a minimum calorie deficit of 500/kcal/day (which increased over time) for an entire year. That would suggest weight loss of 52 lbs per person over the year. Actual weight loss was more like 10 lbs for atkins and 7 lbs for the other diets.
The national weight loss registry data shows that those that have lost a significant amount of weight, and have kept it off, have reduced calories further than those who have always been thin (see the nytimes article linked above).
So, it's not simple, and the truth is, no one has it figured out. If someone tells you they can predict your weight loss based on your diet, ask them for a study that shows it. So far, it does not exist.
I've seen several references say that 3500 calories is about equal to 1 pound of body weight (here's one: http://www.mayoclinic.com/health/calories/WT00011). So, you could just note your rate of weight change at your current calorie intake (that will account for your activity level and metabolism), and then you can predict how that rate of weight change would be affected by changing your calorie intake.
For example, if you're currently holding a steady weight and you cut 500 calories per day (3500 calories per week) from your diet and don't change your activity level, you should end up losing approximately 1lb of body weight per week.
However, as you progress, the same level of activity might burn less calories, or you may put on more muscle, making you more efficient your activity, so that changes things, but this is all approximate anyway.