ZDnet claims the offensive material is being spread via a "linkspam virus" which tempts members to click on a seemingly innocuous story link.
A spokeswoman for Facebook said: "[We are] aware of these reports and we are investigating the issue".
The BBC said that thousands of the site's members have posted comments about the breach on Twitter.
"Discovered a new porn site, it's called Facebook," wrote one user.
"Facebook should do something about the photoshopped porn images, it's offensive," wrote another.
Other users complained they had seen pictures of mutilated animals and people, in some cases adding that they had deactivated their accounts as a consequence.
Several people are linking the attack to the Anonymous hacktivist group after a video appeared on YouTube threatening to "kill" the social network.
However, experts have questioned whether the video was authentic.
Internet security firm Sophos said the images had "flooded" the social network over the past 24 hours or more.