The Subway diet is a marketing campaign by the Subway fast food franchise. It started when a regular customer named Jared Fogle wrote to Subway to report that he had lost over half of his body weight (from well over 180 kg (400 lb) to 86 kg (190 lb)) eating nothing but Subway products every day and a lot of walking. Subway's parent company—interestingly called Doctors Associates Inc. since its founding in the 1970s—jumped on this, of course, and renewed pimping of their inexpensive meal options as a great way to lose weight.
Because of the lack of scientific evidence behind Fogle's success (that is, no observations or controls, and no documentation of any other activities performed or medications taken while on the diet), being supported only by anecdotal evidence for a single person, the Subway diet qualifies as a fad diet. That is not to suggest that Fogle or Subway are deceitful in their motives, but rather that blind faith in a single product line ignores other factors that could be in play.
Subway's association with Fogle ended in 2015 when he was arrested on a variety of charges related to child sexual abuse. Months later, Fogle was sentenced to 15 years in prison for child pornography and sex with underage prostitutes. 
Anyone who bothered to do research above and beyond a cursory glance at the commercials and billboards would realize that Fogle's diet plan was nothing new, and fairly simple. He practiced portion control, eating only six-inch sub sandwiches. He avoided high-fat meats and cheeses, choosing the leaner options (which Subway had already been selling as low-fat) and only drinking diet soft drinks. He also walked to the Subway. Finally, he did it over a long period of time—eighteen months, averaging about 7 kg (15 pounds) per month, which is a bit extreme but not for someone his size.
For a 180+ kg male whose previous diet had included entire pizzas and whole buckets of fried chicken for meals, it doesn't take a doctoral degree in bariatrics to see that he was obviously eating more healthful, low-calorie choices.
Banking on success
Until July 2015, Fogle remained a spokesperson for Subway, and they continue to sell Subway as a healthy choice, assuming you stay away from the meatballs and the bacon. Fogle has been paired with other spokespersons, including Olympic medalist/stoner Michael Phelps. For a short time, Subway even sold flatbread sandwiches and wraps under the Atkins logo, but no longer.
In one of life's creepy coincidences, South Park accidentally anticipated Fogle's shananigans in its episode "Jared_Has_Aides".
The success of this campaign kept marketing gurus on their toes, trying to find similar spokespeople for their own products. In 2009, Taco Bell launched its "Drive Thru Diet" tailored after the story of Christine Dougherty, who lost 25 kg (54 pounds) over two years eating from the Fresca Menu (which was basically their regular menu with no cheese and more vegetables). Raised eyebrows from dieticians forced them to eventually abandon their effort, despite their disclaimer that "[t]he Drive Thru Diet is not a diet plan."