I have recently started a vegan diet (yesterday) and for some reason I wake up this morning to have yellow watery diarrhea. Any connection?
Unlikely. It is unlikely that they are connected, however it is possible that you ate something you do not normally eat, for example the sugar lactose, that your body can not digest well that could cause diarrhea. You should make sure you keep up with your fluids so you do not get dehydrated. If it does not resolve or you are having trouble keeping up with fluids call your doctor.
Maybe. If you switched your diet from regular, eating everything (animal product, dairy, etc.) to vegan, there will be a change in your stool consistency, color and shape, because now your bowel will be digesting a different type of food. It'll take a few days for the adjustment as well. So most likely the yellow watery diarrhea is normal. You'll notice that your stool in general will be softer and large.