Now that the dean of the diplomatic corps, Soviet Ambassador Anatoliy Dobrynin, is about to return home, Manny Levine, former public relations director of Laurel Race Course, remembers meeting him nearly 25 years ago when Dobrynin first arrived in Washington. Levine said he was visiting the Soviet Embassy with John Schapiro, the former president of Laurel. Since several Soviet thoroughbreds had run in the D.C. International at Laurel over the years, Dobrynin was asked if he had any interest in racing. "None whatever," he responded, stating his hobbies were chess and soccer.

Over the years, however, Levine related, the ambassador's interest in horse racing increased, and he did attend several International races when Soviet entries were competing against horses from Europe and the United States. At one point he also joined the Schapiros and the Levines on a visit to Paul Mellon's farm in Upperville to see his thoroughbreds, eight of which have won Internationals. Treasure Trove of Visitors

"The Treasure Houses of Britain" has been such a successful exhibition at the National Gallery of Art that it may soon pass the crowd pleaser of all time, "Treasures of Tutankhamen," which attracted 836,000 during its run from Nov. 17, 1976, through March 15, 1977. As of closing time Sunday, "Treasure Houses" had hit 750,000 visitors since it opened Nov. 3. If it continues at the 7,000-person-per-day rate it has been averaging, by the closing date, April 13, it will have become the most popular show the National Gallery has had. The Impressionists show, another blockbuster, though in much more constricted gallery space, is averaging 3,500 a day. End Notes

Singer Neil Diamond, who is frequently heard on the radio, doesn't work the concert circuit all that often. Now he's on a brief tour and will be at the Capital Centre April 11 for one night. Tickets for the singer, who is a favorite of Princess Diana, go on sale Monday . . . Dave Williams of Cellar Door Productions said he has received word that Kenny Rogers, who was to perform at the Patriot Center March 21, is postponing because of throat problems. The popular singer had throat surgery about a month ago and reportedly hasn't recovered as quickly as expected . . .

Motion Picture Association of America President Jack Valenti will be presenting the Oscar for best foreign-language film at the Academy Awards March 24. It will mark Valenti's 14th appearance on the show, a record The Hollywood Reporter says is surpassed only by Bob Hope with 25 appearances . . .

Comics Billy Crystal, Whoopi Goldberg and Robin Williams will be in town tomorrow to join Sen. Edward Kennedy at a press conference in the Capitol to express their concern for health care for the homeless. The three comedians, who are part of the Comic Relief effort, will join other comics in a telethon March 29 to raise funds for health care for the homeless, with the money raised going to 120 organizations in 18 cities. Washington is one of the cities that will benefit, and one of the organizations here to receive money will be the House of Ruth, which the trio is also scheduled to visit today . . .

Two of rock star Prince's bad-mannered bodyguards who roughed up a photographer who attempted to take a photograph of the singer were sentenced yesterday to two years informal probation and fined $500. They were also sentenced to work 100 hours at a clinic for battered women. They had entered a no-contest plea to the misdemeanor battery charges against them . . .

The fourth annual "Women at the Net" tennis benefit for the Georgetown Women's Tennis Scholarship Fund brought out a celebrity crowd Sunday at Yates Field House at Georgetown University. Among the celebrity contenders were Treasury Secretary James Baker III, Sens. Thad Cochran, Jeremiah Denton, Larry Pressler and John Warner; Frank Fahrenkopf, chairman of the Republican National Committee; Ted Koppel, ABC "Nightline" anchor; and Rep. G.V. (Sonny) Montgomery . . .