Hello.I had the same problem in Borderlands 2 so I made a reddit post asking for help.I found this and this fixed my problem.
Go to your .ini config files directory. On Windows 7, this is Documents/My Games/Borderlands 2/WillowGame/Config.
It's also possible to edit *installDir/Program Files(x86)/2K Games/Borderlands 2/Willow Game/Config
Find WillowEngine.ini (or DefaultEngine.ini)
Ctrl-F to find "WillowScenePostProcess"
Replace with "RyanScenePostProcess"*
You can also set the file to read-only. (not needed)
If you do what I told you to do right above ^^ you can even play with the Anisotropic Filtering at x16.
EDIT:Setting that option to RyanScenePostProcess seems to also give you a FPS Boost.
EDIT 2:Here's the imgur album I made showing my problem.If that's what also happens to you please let me know. Can someone help me out with this ? - Album on Imgur