We just think this is sweet ... Caitlyn Jenner and Kobe Bryant shared a warm embrace after the Vanity Fair Oscar party last night at the Wallis Annenberg Center for the Performing Arts.

Kobe, 40, recently announced he and wife Vanessa, 36, are expecting their FOURTH daughter! The couple have girls Natalia, Gianna and Bianka. Bryant made the announcement on New Year's Day.

Meanwhile, Caitlyn looked stunning in a just-below-the-knee-length gold sequined dress. Girlfriend Sophia Hutchins wore a sexy, sheer black dress -- simply and gorgeous.

We've got TONS of pix of last night's biggest Oscars party ... check 'em out!