Heidi Klum and Seal may or may not be headed for splitsville — it just depends on which site you read.

In a story citing the standard “sources with direct knowledge,” TMZ reports the Victoria’s Secret model and ‘Project Runway’ host will file papers to end her six-year marriage to the Grammy-winning singer sometime next week.

But PEOPLE insiders dispute that, saying that while the couple has been fighting a lot lately, “They have no plans to announce a split right now… They’re not divorcing.” Work obligations have kept the famously affectionate pair apart and allegedly contributed to their marital woes, but now that they’re together again, “they seem to be doing a lot better.”

The couple married in May of 2005 and have a splashy vow-renewal every year. They have four kids between them — three they had together, and one from a prior relationship of Klum’s. Also, the two look like they’re having the time of their lives, throwing over-the-top Halloween extravaganzas, going to Disney World and, just, having a blast.

Here’s a look back at some of the couple’s best moments together, proving that the coolest pair in Hollywood shouldn’t be heading the divorce route.