Sorry but that cabinet should never have been included in a new kitchen design staggered cabinets are already dated and IMO corner cabinets are too. Pictures of the whole kitchen would also help.I am trying to figure out what the cabinets did not go to the ceiling and do you have crown molding all over the rest of the house?

You have no easy solution, your cabinet layout was never designed to have lower crown molding. And, if your current upper cabinets are aligned with doorways, appliance openings, etc., you have zero realistic options to fix this.

Your issue requires that all the upper cabinets be taken down and remounted. As the lower cabinets need a flat surface for their crown molding to die into, your diagonal cabinet needs to be remounted 3" off both the L and R walls. This provides the required flat surface for the lower crown molding, and requires side trim/fillers to cover up the cabinet now being 3" proud of the side walls, but it will also shift all the L and R side cabinets 3" as well. If you have fixed 'monuments' such as appliances, doorways, windows, etc. along those walls, your cabinet layout won't tolerate this shift. At this point you need to tear out the lower side cabinets and reorder new ones of appropriate sizes. It's not a realistic solution. The simple answer is you can't have crown molding on the lower side cabinets.

Thank you for your response. We are updating an 18 year old kitchen, changing the molding to 5” molding & painting cabinets white. We are raising cabinet over cook top to add ornate wood faced vent & changing extremely low desk to buffet height & raising that upper cabinet.

I would remove the gallery rail on top of the cabinets and nix the 5” crown. I’d also skip the ornate faced vent in a nod to less sometimes really is more.

Easiest would be to remove the door and lower the face frame on the corner cabinet to align with the wall cabinets. The extra height will be hidden by the crown.

From what I'm understanding from your comment below, you are planning on raising two other cabinets in this kitchen remodel? I'm thinking that if you do raise the cabinet above the stove and the cabinet above the desk area, you won't be able to add crown to the cabinets anyway, as you'll have the same issue with nothing to dead end the lower cabinet crowns into. Maybe I'm not understanding the plan correctly though.