This paper proposes a new adaptive interference alignment (AIA) scheme in downlink cellular networks. The AIA scheme first selects the degree of freedom (DoF) mode from a set of feasible interference alignment (IA) configurations in accordance with the asymmetric data rate demands fed back from mobile users, which enables base stations to schedule the DoFs among different users. We then derive a unified zero-forcing algorithm to implement perfect IA in closed form, which requires only the feedback of combined channel state information (CSI) rather than that of both the desired and cross links. The proposed method shows good robustness in the case of limited feedback, where, regardless of feedback precision, intercell interference (ICI) can be completely canceled. When data rate demand information is not available, we propose a suboptimal yet effective geometry-based power allocation algorithm (GPA) for the AIA to maximize the sum rate. A two-user case study of power scheduling shows that the proposed Gerschgorin-disc-theory-based GPA significantly improves power efficiency and achieves a comparable sum rate to that of the waterfilling approach, even at a low signal-to-noise ratio.