Fasciation
The strange flattened stems appearing in your cutting bed are not a disease — they are one of botany's more beautiful accidents.
Fasciation is a condition in which the growing point of a plant — the apical meristem — multiplies abnormally, producing a flattened, crested, or ribbon-like stem instead of the usual round one. In the cutting garden, you're most likely to see it in celosias (where it's deliberately bred), zinnias, sunflowers, and occasionally dahlias.
The cause is poorly understood. Bacterial infection (Rhodococcus fascians), random genetic mutation, insect or frost damage to the growing tip, and even viral infection have all been implicated. In most cases it appears once on a single stem and does not spread through the plant or to neighbouring plants — treat it as a curiosity rather than a crisis.
Fasciated stems are striking in arrangements. The flattened, fan-like form is unusual enough to be a talking point. Cut them when you see them — they won't revert — and enjoy the oddity.