Power Supply Diode Keeps Burning Out

The yellow wire from your transformer is connected to the wrong thing. You have it connected to the "Common" in the schematics, but instead it should be connected to two of the diodes.

Your wiring does not look right. It looks like you're using the horizontal strip as the common for the secondary-side circuit. This is obvious because the capacitor grounds there as well as the potentiometer.

But, oops, you have connected one of the wires from the transformer to this common ground.

Note that the schematic has no such junction. The bridge rectifier has four distinct nodes. The transformer connects to two of them, supplying AC, and the other two go to the circuit's voltage rails, supplying DC to it.

In other words, it looks like you may have done this:

And so note how the diode simply shorts out the transformer on every half-cycle, which means that it will be fried from a lot of current.