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Deep learning is overwhelmingly dominant in the field of computer vision and image/video processing for the last decade. However, for image and video compression, it lags behind the traditional techniques based on discrete cosine transform (DCT) and linear filters. Built on top of an autoencoder architecture, learned image compression (LIC) systems have drawn enormous attention in recent years. Nevertheless, the proposed LIC systems are still inferior to the state-of-the-art traditional techniques, for example, the Versatile Video Coding (VVC/H.266) standard, due to either their compression performance or decoding complexity. Although claimed to outperform the VVC/H.266 on a limited bit rate range, some proposed LIC systems take over 40 seconds to decode a 2K image on a GPU system. In this paper, we introduce a powerful and flexible LIC framework with multi-scale progressive (MSP) probability model and latent representation overfitting (LOF) technique. With different predefined profiles, the proposed framework can achieve various balance points between compression efficiency and computational complexity. Experiments show that the proposed framework achieves 2.5%, 1.0%, and 1.3% Bjontegaard delta bit rate (BD-rate) reduction over the VVC/H.266 standard on three benchmark datasets on a wide bit rate range. More importantly, the decoding complexity is reduced from O(n) to O(1) compared to many other LIC systems, resulting in over 20 times speedup when decoding 2K images.