Yes, there are standards, not just for cruise ships but for all marine shipping, and the allowed emission levels were significantly reduced as of January 1 of this year.

Have a read here: http://www.imo.org/en/MediaCentre/HotTopics/GHG/Documents/2020%20sulphur%20limit%20FAQ%202019.pdf

If you can't sleep, spend a few hours Googling "MARPOL VI" and "IMO 2020".

There are two ways to comply with the new emission levels. One is to burn cleaner (and more expensive) fuel. The other is to install scrubbers (less expensive, but then you have to dispose of the scrubbed material). You can probably guess which way many cruise ships went.