The body and frame were completely fabricated from scratch by Clarkaiser Customs. The person who designed it was a Chrysler designer, so it's probably safe to assume it was inspired by what he did at his day job.
It originally had a Cadillac engine, but that was replaced with a 427 Ford later on. There's a good description of the car at coachbuilt.com:
http://www.coachbuilt.com/des/d/didia/didia.htm
He was a life-long car enthusiast and in the early 1950s had the Detroit custom shop of Clarkaiser modify a number of cars for him. Di Dia was influenced by the creations of Alexis de Sahknoffsky and Harley Earl, so much so he that he drove around in a customized Buick with fins. In 1953 he decided to create his own stylized automobile, enlisting the help of his neighbor*, Edward V. Francoise, to put the design on paper.
*(Di Dia lived at 19130 Riverview St., Detroit, MI and Francoise at 19295 Riverview St., Detroit, MI.)
Francoise just happened to be a Chrysler Corp. automobile designer, and Di Dia comissioned him to turn his ideas into a series of renderings which would end up being the car today known as "Bobby Darin’s Dream Car," a vehicle that looked modern a full decade later, and today is considered to be one of the shining stars of 50s design.
It made quite a splash back then, it was in all the car magazines. I've read speculation that the price was exaggerated to help make it seem more exclusive when it was on the show circuit.