At the moment, we don't offer the API option of creating unique faces on the fly. However, as an alternative, you may want to use the "Random" parameter when fetching the images.
You can apply it using the &order_by=random text, with the full request looking like this: curl --header "Authorization: API-Key YOUR_API_KEY" "https://api.generated.photos/api/v1/faces?per_page=1&order_by=random".
As a result, each request will get you a different face from our face gallery, with minimal probability of repetition.