Barack and Michelle Obama appear to be going strong despite ongoing rumors about the state of their marriage ... the former first couple was seen out at dinner Saturday night at Osteria Mozza, a fancy restaurant in Georgetown, in Washington, D.C.

The Obamas' periodic dinner outings have not put to rest rumors about marriage troubles and a possible divorce ... after Michelle was absent from some recent official events, and Barry himself was seen out to dinner without her in March.

The Obamas were warmly greeted by the crowd at the eatery Saturday, with cheers and a round of applause accompanying them as they walked to their table.

What originally seems to have sparked the separation speculation was a 2022 event, when Michelle participated in a forum with Kelly Rowland, H.E.R., Winnie Harlow, and Tina Knowles ... and she talked about a decade of difficulty with her husband. "There were 10 years where I couldn't stand my husband." She pointed out the strife coincided with when their two daughters were very young.

The Obamas have been married since 1992 ... but they haven't been spotted out together a lot this year, despite Barack claiming he's trying to do fun stuff with Michelle.

Earlier this month, the former president was talking to students at Hamilton College and told the crowd he "was in a deep deficit with my wife" after eight years in the White House. Barack added ... "I have been trying to dig myself out of that hole by doing occasionally fun things."

They had dinner in L.A. in December, out at Hollywood hot spot Mother Wolf. In March, we saw Barack at a Los Angeles Clippers game and out to dinner in L.A. without Michelle ... and she wasn't with him at Jimmy Carter's funeral or Donald Trump's 2025 Inauguration. But, they did post pics on social media for Valentine's Day.