I use an old trick my eldest sister taught me to keep the clothes in my closet smelling fresh: open a box of soap and just leave it at the bottom of your closet. When you open your cabinet the next day, you’ll be hit with the scent that isn’t overpowering or too weak, but just right. Of course, make sure you choose a soap with a fragrance that you like.
But if you’re the type who prefers your closet to smell neutral, then I think the Plasmacluster might be your best bet. It’s a system developed and sold by Daiwa of Japan that makes use of ions to get rid of odors and keep your closet smelling clean and fresh.
The negative and positive ions that it releases fasten onto clothes surfaces where the suspended microbes are, forming oxidizing hydroxide radicals. This instantly causes the removal of hydrogen from the proteins, which causes the physical breakdown of the microbes, rendering them inactive, giving you a clean, nice-smelling closet.
Unfortunately, the Plasmacluster system costs ¥45,990 (~$558 USD). We have no idea on whether or not it actually works, though, so you might end up spending close to half a grand just to see if it does. Or you could just buy a box of soap.