Study Suggests Superiority of Dieting With 2 Refeeds/Week vs. Continuous Dieting - In Spite of Lower Energy Deficits !

This is not the kind of refeed I would suggest - irrespective of how effective refeeds are using all of them to pig out to the extremes will be counter-productive.

There are three purported benefits of "refeeding", i.e. having 1-2 days per week where you eat as much as you want, regularly, while you're dieting. The refeeds are supposed to (1) prevent your metabolism from shutting down to ensure continuous fat loss, (2) help maintain lean mass and (3) reduce the weight rebound when you return to an energy sufficient diet.

Yes while the efficacy of this practice has been demonstrated before (more), previous studies did not have an appropriate control group that would allow us to say for sure whether dieting continuously wouldn't have yielded the same results.
To change that Radhika V. Seimon and colleagues from the Sydney Medical School conducted a preliminary, but highly interesting rodent trial. In said study, male C57/Bl6 mice that had been rendered obese by an ad libitum diet high in fat and sugar for 22 weeks were then fed one of two energy-restricted normal chow diets for a 12-week weight loss phase.

• The continuous diet (CD) provided 82% of the energy intake of age-matched ad libitum chow-fed controls. 
• The intermittent diet (ID) provided cycles of 82% of control intake for 5–6 consecutive days, and ad libitum intake for 1–3 days. 

In conjunction with the group on the control (CAC) and the group on a continuously obesogenic diet (CAF), that's a total of four diets. In that, the control diet (CAC) was necessary, because the data was used to calculate the efficacy of the CD and ID diets as (total weight change) ÷ [(total energy intake of mice on CD or ID)–(total average energy intake of controls)] - or, in other words, weight change divided by calorie deficit.

Figure 1: Study flow chart. CAC, continuous ad libitum chow; CAF, continuous ad libitum high fat; CD, continuous diet; ID, intermittent diet (Seimon. 2016).

To be able to determine any long(er)-term effects that would effect the rodents weight after the diet, a subset of mice underwent an additional 3-week weight regain phase involving ad libitum re-feeding, as a model for returning to an energy sufficient ad libitum (eat as much and what you want).
As you can see in Figure 2, both the ID and CD group lost a significant amount of weight during the weight loss phase. In that, it is quite remarkably, though, that (a) the intermittent diet (ID) phase created a continuous up and down, and that (b) the continuous dieting group lost almost all the weight in the first fifth or fourth of the dieting phase, while the intermittent diet group lost its weight continuously (albeit with mini-rebounds / probably water / during refeeds).

Figure 2: Body weight development (g) over the 22+12+3 week weight gain, loss and regain phase (Seimon. 2016).

Eventually, both groups ended up at virtually identical weights at the end of the weight loss phase. Since the ID group achieved this weight loss with ~11.5% higher energy intakes (due to the refeeds) than the CD group, their calculated weight loss efficacy was a whopping 2.3x higher - or, as the scientists phrase it:

"During the weight loss phase, there was a significant, 2.3-fold greater weight loss efficiency (total weight loss total energy deficit) for mice on the intermittent diet compared to those on the continuous diet. This is because whereas both groups of energy-restricted mice exhibited similar total weight loss (Fig 2), the total energy deficit of mice on the inter mittent diet during the 12-week weight loss phase (304.5±47.7 kJ) was less than half that of mice on the continuous diet (646.9±16.8 kJ). This means that for every kJ of deficit in energy intake relative to the energy intake of age-matched control mice, mice on the intermittent diet lost 2.3 times as much weight as mice on the continuous diet (Seimon. 2016)."

No such significant difference was observed for the weight regain and the body composition, though. While the mice in the CAF group were obviously the fattest and kept gaining weight continously, the the fat mass of the mice in the intermittent and continuous diet groups did not differ significantly after dieting and were in fact similar to that of the lean rodents in the control (CAC) group.

Figure 3: Body composition as determined by dual energy X-ray absorptiometry. (A) Fat mass (g), (B) fat mass (% of body weight) and (C) lean mass (g) at the end of the weight loss and weight regain phases. CAC, continuous ad libitum chow; CAF, continuous ad libitum high fat diet; CD, continuous diet; ID, intermittent diet (Seimon. 2016).

And while, at the end of the weight regain phase, fat masses of mice in the continuous and intermittent diet groups remained statistically indistinguishable from each other, the data in Figure 3 suggests a minimal advantage in terms of the fat to total mass ratio, i.e. the body fat % after the weight regain phase - not enough to confirm supposition (3) that refeeds would help "reduce the weight rebound when you return to an energy sufficient diet", but worth mentioning, anyways.

That's also because the differences in the intermittent and continuous diet groups' glucose and insulin levels may not be significant, but they exist with the ID group suffering a sign. less pronounced reduction in insulin (way below control) during dieting and had 15.7% lower insulin levels after the weight regain phase - all that at stable (=group-equivalent) serum glucose levels.
References:

• Seimon, Radhika V., et al. "Intermittent Moderate Energy Restriction Improves Weight Loss Efficiency in Diet-Induced Obese Mice." PloS one 11.1 (2016).