"Despite fact" is a phrase used to express something that is true despite a contradictory circumstance. Synonyms for this phrase include "notwithstanding the fact," "regardless of the fact," "even though," "albeit," "although," and "notwithstanding." These phrases all convey the same meaning as "despite fact," but may be used in different contexts depending on the speaker's intent. "Notwithstanding the fact" is a more formal way of expressing "despite fact," whereas "even though" and "although" may be used more casually. Ultimately, the choice of synonym depends on the speaker's tone and the emphasis they want to place on the contradictory circumstance.