noun, na-adjective
free and uncontrolled; freewheeling; totally uninhibited
Describes a person or behavior that is completely unrestrained, spontaneous, and free-spirited, often with a positive or neutral connotation. Can be used as a noun or na-adjective.
彼の奔放自在な生き方に憧れる人も多い。
Many people admire his freewheeling way of life.
その画家は奔放自在に筆を走らせた。
The painter moved the brush with total abandon.
自由奔放 is more common and emphasizes freedom and lack of restraint, while 奔放自在 adds a nuance of complete self-direction and spontaneity.
Compound of 奔放 (free, unrestrained) and 自在 (free, at will). The exact historical derivation is uncertain, but the combination reinforces the idea of complete freedom.