I've always had thin skin under my eyes which means I sometimes looks like I got double punched. Concealer is the only thing that really works for me, and that's a shame because I like going makeup-free a lot. I've never found a treatment natural or otherwise that works 100% for me, but I know that vitamin K is
supposed to help circulation which could help diminish the look of the capillaries under the delicate eyes skin.
Good natural sources of vitamin K are spinach (particularly frozen), turnip greens, cooked or frozen kale, and cooked or frozen collards. An alphabetical list of foods and their vitamin K content is available
here.