The design of mean and variance schedules for the perturbed signal is a fundamental challenge in generative models. While score-based and Schrödinger bridge-based models require careful selection of the stochastic differential equation to derive the corresponding schedules, flow-based models address this issue via vector field matching. However, this strategy often leads to hallucination artifacts and inefficient training and inference processes due to the potential inclusion of stochastic components in the vector field. Additionally, the widely adopted diffusion backbone, NCSN++, suffers from high computational complexity. To overcome these limitations, we propose a novel target-based generative framework that enhances both the flexibility of mean/variance schedule design and the efficiency of training and inference processes. Specifically, we eliminate the stochastic components in the training loss by reformulating the generative speech enhancement task as a target signal estimation problem, which therefore leads to more stable and efficient training and inference processes. In addition, we employ a logistic mean schedule and a bridge variance schedule, which yield a more favorable signal-to-noise ratio trajectory compared to several widely used schedules and thus leads to a more efficient perturbation strategy. Furthermore, we propose a new diffusion backbone for audio, which significantly improves the efficiency over NCSN++ by explicitly modeling long-term frame correlations and cross-band dependencies.