Will Smith and wife
Jada Pinkett Smith have bounced back from the separation rumors that plagued them earlier this year ... and TMZ has learned it was differing opinions on how to manage their superstar kids that caused the original strife.
Sources close to the couple tell TMZ they are doing "wonderful" now -- but earlier this year, sources tell TMZ there was tension between the two over how best to manage the careers of
Jaden and
Willow.
We're told each had their own ideas for how things should be handled -- with Will pushing more for full-blown stardom and Jada leaning towards easing them in to things.
But our sources say that bad patch -- which included rumors Jada
had an affair with
Marc Anthony -- is now past them and things are back to normal.
Will's rep had no comment.
Will Smith and
Jada Pinkett Smith just released a joint statement SHOOTING DOWN a report that
they have separated.
The statement reads, "Although we are reluctant to respond to these types of press reports, the rumors circulating about our relationship are completely false."
The two add, "We are still together, and our marriage is intact."
"
Karate Kid"
Jaden Smith and his fit pops
Will Smith proved the up & coming apple doesn't fall far from the A-list tree while on the beach in Hawaii on Thursday.
The vacationing Smiths will be celebrating as Jaden turns a whopping 13 today.
Jaden and
Willow Smith didn't just bump into
MJ's kids on a movie set in L.A. yesterday -- TMZ has learned, it was all set up by
Katherine Jackson ... to help nudge her grandchildren in a positive direction.

Sources close to Katherine tell TMZ, she believes the Smith children are prime examples of young success in Hollywood -- both extremely talented and down-to-earth -- and thinks
Prince,
Paris, and
Blanket could learn a lot from them.
According to sources, Katherine wants to surround her grandchildren with role models like Jaden and Willow -- so she set up the meet-and-greet ... and we're told, the kids got along like a house on fire.
Katherine wants Michael's kids to enjoy their childhood -- and is actively encouraging them to become involved in all kinds of activities ... including acting.
It was a meeting of the A-list celebuspawn as
Michael Jackson's three kids (
Paris,
Prince and
Blanket) hung out with
Will and
Jada Pinkett-Smith's children,
Willow and
Jaden Smith, on an L.A. film set the other day.

The Jackson kids arrived to the set with their grandmother,
Katherine Jackson. So far, it's unclear if the kids were on the set to act ... or just to hang out with the Smiths.
As we previously reported, the Jackson kids have expressed a serious interest in Hollywood -- earlier this year, Prince told "
Good Morning America" he was "looking at a couple of opportunities in show business ... mostly producing."
He's only 12 years old -- but last year,
Jaden Smith pulled in SEVEN FIGURES to star in "
Karate Kid" ... TMZ has learned.

TMZ obtained Jaden's "KK" contract from June 2009 -- back when he was only 10 -- and according to the docs, his up-front fee was split into two installments ... one for $900,000 and one for $100,000.
But Jaden's back end deal was even more lucrative -- since the film topped $150 million in the domestic box office, the young actor locked down another $2 million bonus.
But $3 million is the bare minimum -- based on several additional in-contract perks AND the astronomical success of the film, Jaden likely pulled in even more.
He's still the poorest person in his family.
Jaden Smith is ALIVE -- very alive -- despite some sick, stupid BOGUS Internet report that he died in a snowboarding accident in Switzerland.

Just like
Will Ferrell, Adam Sandler, Jeff Goldblum, Urkel and Pat Sajak ... some moron published a FALSE report thinking it would be funny.
But Smith's rep tells us, "It's absolutely not true."
So, there ya go ...
Jaden Smith.
1998 - ???
These crazy kids today with their Facebook and their video games and their iPhones ... and their boat parties in Hawaii with chicks in bikinis.

Humpf.
Justin Bieber and
Jaden Smith aren't usually rivals -- but TMZ has learned the two young superstars went toe-to-toe a few nights ago ... in the form of a dance-battle at a NY bowling alley.

TMZ has obtained pictures of Biebs, 16, and Smith, 12, in action at the
Lucky Strike Lanes & Lounge on Tuesday night ... following their concert at Madison Square Garden.
We're told the dynamic duo got down to
Kevin Rudolf's song "You Make the Rain Fall" -- and the whole thing was captured on tape by Bieber's documentary crew.
Our sources say both guys "killed it" on the dance floor ... but we're told Bieber was the clear winner ... when he busted out a moonwalk!