You've gotten some great advice, so I won't repeat any of that here. I will just say that, in addition to milk and juice, we discovered the hard way that gluten is a very common problem for kids that all-too-often is overlooked.
My son appeared to be health and thriving at that age, too. He was big for his age and energetic and rarely sick. But somewhere between 15 and 20 months as he ate more and more solids, his stools changed. At first I thought it was a stomach bug, but as the diarrhea persisted I began to realize it was something else. It was runny, slimy, full of undigested or partially-digested food, and really smelly. It resembled what a friend of mine had described with her son before they discovered that *he* was gluten intolerant.
Long-story-short, we discovered that not only does my son have Celiac Disease (genetic gluten intolerance)but so does my husband, my other 2 children have the gene although at least one of them hasn't shown signs of developing the disease yet, and my father may also have it. In fact, estimates now are that 20% of people may in fact be Celiac, even though the numbers of diagnosed aren't that high simply because it is hugely under-diagnosed and many doctors don't recognize it when they see it.
So, if the diarrhea doesn't resolve itself within another week or so, I would recommend trying a gluten-free diet for a couple of weeks. Clinical tests for the disease are unreliable in children under 5, so the best way to determine gluten sensitivity is to do a trial of avoidance. In a child that young, you should see a rapid recovery if it's an issue. All my son's symptoms resolved within the first week and he was like a new kid. In fact, issues we didn't think were related also resolved, such as a fussy temperament, sleep disturbances we'd thought were teeth, a slight speech delay, and flatulence. His eating habits also improved.
If you decide to try this but feel overwhelmed or don't know where to start, feel free to email me. It's SO MUCH EAASIER than I thought it would be: and this from someone who now has an entirely gluten-free family!
Best of luck!