The original Ugly Duc was my 1974 750 GT. It didn't take long for that bike to lose it's ugly duck status though, since it's ugliness grew from having been neglected for so long. The bike was rather attractive from the factory - mine only needed a "little" freshening up.
These are a different story. The new Ugly Ducs are a 1966 250 Monza (yellow), and a 1966 160 Monza Jr. (red). These are in about the same condition as my 750 was, but they are from an era that most people agree wasn't exactly the high point of Italian style at Ducati. The fundamentals are there though. I'm sure there are a couple of good looking bikes hidden underneath that squared off bodywork.
The concept for the 160 is something along the lines of a 175 TS, with valanced fenders and rounded bodywork. This project is well underway so it's look is pretty much set, click on any of the 160 pictures for more details.
The 250 is going to be a Bitsa. Basically a solo seat, upgraded front brake, rearsets, and a few engine mods. That got me started collecting other parts too. A 35mm fork, an Oldani style 2LS brake, a Mach 1 tank, flanged alloy rims, and a 350 engine. In time the Mach 1 tank was sold and replaced by a tank (and tail) by Evan Wilcox, I decided not to use the 35mm forks, and discovered the rims aren't drilled correctly for the front hub so they'll be changed too.