Optimal adaptive quantization is one of the key points to optimize the coding efficiency of video encoders. The latest block-based video compression standards, such as high-efficiency video coding (HEVC), extensively use predictive coding techniques that create dependencies between blocks and increase the complexity of optimal block quantizers search. Specifically, the motion compensation is responsible for a dependency network connecting all blocks of the same GOP together. In this paper, this dependency network is estimated by a temporal distortion propagation model and an accurate estimation of Inter and Skip modes probabilities. Optimal quantizers are then designed per block in order to achieve global optimization in terms of rate-distortion efficiency. By implementing the algorithm into the HEVC reference model (HM), we report -16.51% PSNR-based and -26.26% SSIM-based average bitrate savings compared to no adaptive quantization. The proposed algorithm outperforms several related methods from the state-of-the-art. Moreover, along with the demonstration of an optimal quantizer solution, we propose an in-depth analysis of the algorithm behavior. This analysis includes, among others, the relative distribution of rates between frames and the control of quantizers dynamic range.