I've been jogging and walking while wearing a diaper too.
It really is a good thing to wear a diaper while jogging, walking, running etc as the diaper means you can just go pee or poop.
I've also done both in my diaper while jogging, walking and running.
Just make sure to wear a good quality adult diaper while out jogging or walking or running so the diaper does not start breaking down as in the absorbent material doesn't start falling down inside the diaper.
That happened to me with a cheap adult diaper.
But the thicker, plastic backed adult diapers with more SAP in them hold up well to the Jogging, Walking and Running.