How can I prevent iTunes from automatically downloading podcasts? I listen to podcasts, but almost always on my iPhone (by downloading them on the iPhone directly) and almost never on my computer through iTunes. I do sync my iPhone with iTunes. However, any time I open iTunes, it tries to automatically download new podcast episodes. Is there a way to prevent this?

I tried plugging in my iPhone, going to the Podcasts tab, and unchecking Sync Podcasts, but this resulted in a dialog box asking if I'm sure I do not want to sync podcasts, and informing me that if I continue, all existing podcasts on my iPhone will be deleted. That's not my desired result, of course.
For anyone coming across this now, in the latest version of iTunes (~v12.5.1) it's much easier to prevent downloads for all podcasts you're subscribed to. 

Steps:


Go to "Podcasts" in the menubar dropdown. 
In the second column of your subscribed podcasts, at the bottom there's two buttons, "Refresh" and "Defaults...", click "Defaults..."
In the popup, set "Download Episodes" to "Off".