No. It is a semi-tropical plant not inclined to self sow. Even in my very mild climate it has never set seed. The plants do increase in size but are not aggressive spreaders.

You should be aware that like all other euphorbias, using it for a cut flower will release the white latex sap that many find to be at the very least a skin irritant and with others, a serious toxic reactivity. Be sure to wash hands very thoroughly and keep away from your face

i have the green and yellow version ... it moves around ... acting almost like a biennial .. old plants dying ...

but i would never describe it as taking over ...

based on your location .. which you havent provided.. i have no clue how it will act for you ...

the link calls it an annual.. and states further: Self-cleaning, no deadheading necessary.

which i might interpret to mean.. its sterile ... but thats just a guess ..

ken

https://www.provenwinners.com/plants/euphorbia/diamond-frost-euphorbia-hybrid