How do I set up Braid to use a gamepad on PC?

So I asked this question about Braid on PC/PS3 a while back, and one of the answers pointed me to the MotionInJoy drivers that allows PS3 controllers to be used on a PC. I've installed them properly and have used my DualShock 3 in a few games, but I can't figure out how to enable it when I'm playing Braid!

There doesn't seem to be any menu item to select an input type, which begs the question - is Braid not detecting my controller for some reason, or does Braid simply not allow you to use anything but the keyboard for input?

Solution 1:

Braid is described on Steam as having support for the Xbox 360 controller, which MotionJoy is able to emulate. Try using that.

Solution 2:

You could try JoyToKey and map keypresses to your PS3 gamepad. I never played Braid so I don't know much about its input support.