Kim Kardashian -- Conflicted Over Divorce, Flies to Minnesota

Kim Kardashian left for Minnesota last night to see Kris Humphries ... and sources connected with Kim tell TMZ she is conflicted over the divorce.

We got pictures of Kim as she made her way through the Minneapolis-St. Paul International Airport at around 5:30 AM local time. We're told Kim flew commercial and was traveling with the guy in the photo (above, left) who appeared to be a bodyguard.

According to our sources, Kim booked the flight very last minute (see her below at LAX) because she felt like she owed it to Kris to talk things through with him face-to-face. We're told no reality show cameras were involved.

Our sources tell us ... Kim has been saying even before she filed for divorce that she wasn't sure about ending the marriage. As we first reported, she was crying on and off last weekend before she decided to pull the trigger.

Sources say it's definitely not accurate to call this a reconciliation ... or even an attempt at one ... but the door is definitely not shut.

Sources tell TMZ ... Kris and Kim will be meeting with the pastor who married them to talk about the marriage, the divorce, and their feelings. Again, this is not a reconciliation but we're told Kim wants to make sure she and Kris have closure and talk everything out.