There are various plants with the common name "corn flower"

Some are annual and one at least ( Centaurea) is perennial

Usually annuals, but they can seed themselves if left to do so.

Cornflowers are one of the true biennials

The commonest annual cornflower has flowers about 2cm across. The perennial one, Centaurea has much bigger flowers, more like 50cm, and it has big glaucous green leaves, whereas the annual has little thin ones. You won't have to dig up the annuals as they will just die down. You may be driven to digging up the centaurea if you are short of space!