Amphiphilic block copolymers with complex topologies (e.g., star and brush topologies) have attracted significant attention in drug delivery owing to their superior performance over linear micelles. However, their precise synthesis and structure-property relationships require further investigation. In this study, hydroxylated polybutadiene with adjustable topology and hydroxyl group density was employed as a macroinitiator to synthesize well-defined amphiphilic poly (ethylene oxide)--poly(-caprolactone---valerolactone) (PEO--P(CL--VL)) copolymers via ring-opening polymerization (ROP). A series of linear, star, linear-comb, and star-comb copolymers were prepared as curcumin-loaded micellar carriers for the study. The self-assembly behavior, drug encapsulation efficiency, and in vitro release profiles of these copolymers in aqueous environments were systematically investigated. The results demonstrated that increasing the branch length of star-comb copolymers effectively reduced micelle size from 143 to 96 nm and enhanced drug encapsulation efficiency from 27.3% to 39.8%. Notably, the star-comb architecture exhibited 1.2-fold higher curcumin encapsulation efficiency than the linear counterparts. Furthermore, the optimized star-comb nanoparticles displayed sustained release kinetics (73.38% release over 15 days), outperforming conventional linear micelles. This study establishes a quantitative structure-property relationship between copolymer topology and drug delivery performance, providing a molecular design platform for programmable nanocarriers tailored to diverse therapeutic requirements of various diseases.