KK threw up an IG in Tristan's honor, wishing him well as hits the big 3-2 ... and showering him with sweet words that certainly paint him as a great dad and family man. She writes, "Happy birthday @realtristan13. You are truly the best father, brother & uncle."

She continues ... "Your love, attention, silly dances, hugs, carpool rides, bed time rituals, the way u show up for them. All of the above means more than you’ll ever know to your family of littles."

And finally, Khloe has a bit of a message for Tristan ... which seems to touch on his repeated cheating fails over the years. She writes, in earnest, "My birthday wish for u is that u continue to crave change, healing, and transformation. Be strong, be kind, be patient, be free. Continue to Make your soul and your mommy proud. Happy birthday baby daddy."

By the sounds of it ... Khloe seems convinced that Tristan is on a good path, and that he's dedicated to doing better. What that means for them romantically, well, hard to tell.

We know Khloe and Tristan hang out a lot because of their 2 kids -- but she also appears to be at his side for unrelated reasons too ... including the death of his mother, for which she flew out and attended the funeral. Of course, they were out this weekend too.

Remember, Tristan tagged along for the Haqq sisters' birthday bash, Khloe's BFFs ... so maybe they're working toward a reconciliation after all. In any case, Khloe's still got warm feelings for TT.