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Importance weighting (IW) is a golden solver for joint distribution shift, where the joint distributions differ between the training and test data. To solve this problem, IW estimates test-to-training density ratios as importance weights and reweights the training losses accordingly. Recent advances in dynamic IW (DIW) integrate weight estimation into model training, enabling scalable IW for deep models and achieving strong performance on large modern datasets. Despite its promise, DIW remains limited in two aspects. First, it incurs substantial computational overhead by solving a kernel mean matching (KMM)-induced optimization problem to convergence in every mini-batch. Second, it relies solely on KMM for weight estimation, whereas the IW literature contains diverse estimation methods based on different divergence measures. In this paper, we propose accelerated DIW (ADIW), a unified and efficient IW framework for deep learning under joint distribution shift. ADIW performs a few lightweight projected gradient descent updates that warm-start from previously updated weights, substantially improving efficiency. Moreover, ADIW generalizes DIW into a unified divergence-minimization framework that supports diverse weight-estimation methods in a plug-and-play manner, including those based on the Kullback-Leibler divergence, squared distance, and Wasserstein-1 distance. We establish convergence guarantees for ADIW under mild conditions, and empirical results demonstrate that ADIW achieves state-of-the-art IW performance while being substantially more efficient.