EXCLUSIVE

Kobe Bryant's wife Vanessa caught the NBA star "very recently" in the latest act of infidelity, and that is why she filed for divorce ... sources directly connected with the couple tell TMZ.

Our sources would not tell us how Vanessa caught Kobe, but we do know it was NOT through text messages a la Tiger Woods.

We're told Vanessa had caught Kobe with "multiple women" over the years ... but his latest affair was the straw that broke the camel's back ... and she felt she needed to finally end the marriage.