Drinking too much water in a short amount of time could cause Diarrhea since the water won't be absorbed properly by the body.
When the water isn't absorbed by your body the water will then collect in your body since it's unable to get rid of the excessive water and then can lead to vomiting, nausea and yes diarrhea.
In some cases drinking too much water at one time can be fatal and it's what is called water intoxication.
It's good to stay hydrated when you already have diarrhea since too much diarrhea can dehydrate you but if you drink too much water while having diarrhea it can make the diarrhea worse.