Although Honorine Jobert anemones do grow vigorously, they are not considered invasive in most of the United States. However, these plants will naturalize to form a large colony, so give them plenty of room to grow. Some gardeners avoid planting Japanese anemones near other perennials, as their underground spread is vigorous and they may overtake their neighbors. If you don't want your anemones to spread, be sure to divide and remove rhizomes every few years.