The antonyms of 'tying down,' which means restricting or confining something or someone, are 'freeing,' 'loosening,' 'liberating,' and 'releasing.' Instead of immobilizing or constraining, freeing entails letting go of restraint or hindrance. Loosening, on the other hand, means relaxing or making something less tense or rigid. Liberating suggests setting someone or something free from captivity or bondage. Releasing, on the other hand, implies allowing something or someone to escape or depart from existing confinement. These antonyms connote a sense of freedom and liberation, allowing individuals, ideas, or objects to move and grow freely.