Triply periodic minimal surfaces (TPMS) are attractive building blocks for lightweight architected materials, yet exploring their morphology under area- or Willmore-energy objectives with explicit volume constraints remains challenging. We propose an isogeometric reaction–diffusion B-spline level-set framework for TPMS design within a unified optimization loop. The geometry is represented by a level-set field on a three-dimensional B-spline grid, enabling consistent evaluation of surface area, curvature, and volume fraction. The evolution equation follows from a curvature-regularized shape gradient of an area or Willmore functional with a volume constraint and leads to a fourth-order reaction–diffusion flow. A Lagrange-multiplier bisection scheme enforces the prescribed volume fraction, while symmetry filtering and bandwidth control restrict the design space and suppress high-frequency artifacts. A semi-implicit time discretization with a preconditioned conjugate-gradient solver yields a stable algorithm that avoids ad hoc reinitialization of the level-set field. Numerical studies on cells with Schwarz P, Schwarz D, and Schoen G symmetries reveal a two-stage evolution: rapid regularization with volume locking and curvature decay, followed by plateaus in which small residual updates may trigger transitions to lower-area configurations. The framework recovers classical TPMS families, discovers additional candidates, and provides a promising design tool for TPMS-based architected materials.