This plant is native to China and Korea, and like many of my favourite plants, such as vanilla leaf, bloodroot, or the umbrella plant, Darmera peltata, is as much or more appreciated for its foliage as its flowers.
The leaves can expand to two feet in diameter, and are a pleasing pale green --they almost make the gout weed look good! The leaves of A. tabularis are similar in form to those of Darmera, a native of California and Oregon, and both are in the Saxifragaceae, a family big on leaves, not so big on blossoms. Both plants like moist conditions, and do well near ponds or other water features. Astilboides tabularis was previously placed in the genus Rodgersia (was known as shield-leafed Rodgersia), another Asian genus of saxifrage with eye-grabbing foliage.
So I urge on my Astilboides, a diamond in the rough, hoping it can shade out the invasive plant, but doubting it can. I may have to dig up that whole area yet, but I'll wait until fall, after the large round leaves have dropped.