Personally, I would paint the cabinets in a heart beat. A warm medium gray on the base cabinets, light gray on the walls, and a creamy white on the uppers.

Second, I would remove that very odd crown moulding trim on the ceiling above the window...it detracts from your cabinet crown.

How about iridescent tiles ? They would have some red tones to match the cabinets and reflect light.

Install recessed lights in the ceiling and under cabinet lights for additional task lighting. If you don't need the curtains for privacy, I would remove them. I too have cherry cabinets and uba tuba granite and it is a struggle to keep it from looking too dark.

I also agree about removing the crown molding from the window, it competes with the cabinet design. I think a glass tile black splash would help reflect the existing light in the kitchen. I do think your kitchen would benefit from more natural light, if you don't have an obstruction above the kitchen, I'd suggest one of the solar tubes to reflect more natural light into the space

I know you asked about backsplash colors that would lighten the room, but I also wanted to show you a kitchen I love that looks very much like yours but with a beautiful 4" slate tile backsplash. It's not lighter, but I find it very beautiful:

Agree on the under-cabinet lighting and we are discussing a skylight to add more light. Also, should mention the kitchen is not super large...so while the combo is classic, it makes the room feel even smaller.

Finally, a very light backsplash option. And if you aren't looking to tile the backsplash, you could choose a very pale gray paint color for the walls:

Gorgeous kitchen feeny!

Would it be possible to cut out the center panel in one or two doors and replace with a frosted or patterned glass? In the kitchen that feeny shows, I think the open shelving helps break up the long expanse of dark wood. One or two glass door cabinets would do the same thing IMO.

I vote for a light glossy backplash tile, even an iridescent as mentioned above, and most importantly run it all the way around the window and up to the ceiling also--get rid of that odd piece of crown. Adding luminosity and shine will instantly help with lightness.

Love these options for tile...
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Love the cabinets and counter top..don't change them. The back splash has a difficult start & stop point when you get to the window wall. I would remove the crown piece and paint the entire back splash, wall & CEILING one color. Something that would go with the rest of the colors in the house. Maybe a light sage green, a light yellow, whatever. Add a light color print fabric (maybe large trellis pattern) roman shade on the window and an interesting light coordinated colored rug on the floor. It would brighten the space and distract the eye from all the dark, every room needs pattern. You have a great start. Good luck to you.

Technically it is not a big deal . The problems is it may looks strange .
The glass doors doors should be custom made. It is not a big deal to make it .
The problem is to match the existing stain with new one , which is extremely hard when doors located next to each other . Generally it may not worth it , because finishing .

I agree with Barbara- I am a designer also. If you can add more lighting, that would also be advised.

White subway is an option if you don't want to paint your cabinets although i think the main thing making your kitchen look dark is because your cabinets are dark. Paint it white and watch your kitchen look brighter without having to change anything else.