This dissertation proposes a new framework for phase estimation that overcomes these limitations and demonstrates its effectiveness across multiple DNN-based SE models. We begin by introducing the first deep state-space-based SE model operating on complex-valued spectrograms. While it surpasses baseline models with a compact U-Net architecture, its estimated phase offers limited improvement over the noisy phase, underscoring the difficulty of direct phase prediction. To address this, we develop a novel explicity consistency-preserving loss that leverages the observation that perceptually high-quality speech arises when magnitude and phase are mutually consistent. Building on this insight, we integrate geometric constraints under additive noise conditions with the consistency principle, resulting in the Multi-Sourced Griffin-Lim Algorithm (MSGLA). MSGLA jointly refines speech and noise phases through iterative updates guided by DNN-estimated magnitudes and geometric relationships, outperforming direct phase estimation and prior geometric methods. Finally, we extend these ideas to a large-scale generative pretraining framework that models the distribution of clean speech spectrograms and incorporates the consistency-based phase loss during training.