CERTIFIED CONSTRAINT LIFECYCLES FOR TRAJECTORY-PROXY VIDEO DIFFUSION CONTROL

Constraint timing poses a dilemma in reverse denoising: later updates can violate previously satisfied constraints, while premature protection can hinder progress on unmet ones. To address this tension, we introduce Certified Constraint Lifecycles (CCL). CCL formulates inference-time diffusion control as an admission-preservation lifecycle under evolving protection obligations: qualifying observer-supported satisfaction on realized post-update states triggers irreversible gate-level admission, and the accumulated commitment state determines which protection relations and nonlinear endpoint checks apply to subsequent denoising updates. For differentiable trajectory proxies, CCL projects the sampler proposal onto the one-sided first-order cone induced by the exposed Jacobian and then applies a finite-step nonlinear guard. For successfully completed transitions, we prove guarded commitment invariance: every admitted proxy commitment remains satisfied. At a fixed state and proposal, with the exposed Jacobian evaluated exactly, we derive an exact pre-guard decomposition of the feasible row-space motion retained by one-sided protection but removed by equality protection. Controlled experiments show that CCL more reliably achieves and maintains trajectory-proxy satisfaction while reducing collateral deviation under matched final proxy satisfaction.