Recent learning paradigms aim to enforce idempotency in generative models by ensuring repeated application leaves samples unchanged on the target data manifold. However, many existing approaches fail to achieve exact fixed points, resulting in instability and drift during repeated applications. The authors identify a geometric mismatch between encoder and decoder manifolds as the primary cause of this failure. To resolve this, they propose a training framework that explicitly aligns the geometry of both components to learn consistent representations of the same underlying data manifold. This alignment encourages stable projections and significantly reduces idempotency error compared to prior methods. Empirical results demonstrate that the approach consistently regenerates identical outputs under repeated application for both image generation and editing tasks. Furthermore, enforcing this type of idempotency improves identity preservation and information stability in generative models.