I actually looked into this quite a bit recently. I searched websites documenting all of the separate instances of rape in Germany involving refugees (like this one). Admittedly it looks like a lot.

It turned out, however, that the rates of rape weren't significantly different from Germany's pre-refugee influx numbers. The refugees alone had just over 10 reported rapes per 100,000 where the general public in 2012 had 9.985 per 100,000 people. For some perspective, the US national rate in 2014 was 26.4 per 100,000 . (There may be some legal difference, but I'm no expert)

So yes there are shitty people, but surprisingly less shitty people than I had expected from the news coverage. What we may be seeing are a few things: added attention due to the stress from the situation and suspicion, news websites re-posting and pushing the same story, outrage at the government's attempted coverups/ failure to prosecute, and outrage at policy failure. There's a lot of rightful outrage to be had, rape is bad no matter what and the government failing by trying to cover it up or failing to prosecute the crime is very contemptible. I've heard this described as a rape epidemic though, and I'm not sure I would.

If anyone has more comprehensive info, I will take a look and update the numbers. But so far I wouldn't call it an epidemic, just they are a bad more awful than the regular Germans, but not as awful as America.