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Recently, high dynamic range (HDR) image reconstruction based on the multiple exposure stack from a given single exposure utilizes a deep learning framework to generate high-quality HDR images. These conventional networks focus on the exposure transfer task to reconstruct the multi-exposure stack. Therefore, they often fail to fuse the multi-exposure stack into a perceptually pleasant HDR image as the inversion artifacts occur. We tackle the problem in stack reconstruction-based methods by proposing a novel framework with a fully differentiable high dynamic range imaging (HDRI) process. By explicitly using the loss, which compares the network's output with the ground truth HDR image, our framework enables a neural network that generates the multiple exposure stack for HDRI to train stably. In other words, our differentiable HDR synthesis layer helps the deep neural network to train to create multi-exposure stacks while reflecting the precise correlations between multi-exposure images in the HDRI process. In addition, our network uses the image decomposition and the recursive process to facilitate the exposure transfer task and to adaptively respond to recursion frequency. The experimental results show that the proposed network outperforms the state-of-the-art quantitative and qualitative results in terms of both the exposure transfer tasks and the whole HDRI process.