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We seek to reconstruct sharp and noise-free high-dynamic range (HDR) video from a dual-exposure sensor that records different low-dynamic range (LDR) information in different pixel columns: Odd columns provide low-exposure, sharp, but noisy information; even columns complement this with less noisy, high-exposure, but motion-blurred data. Previous LDR work learns to deblur and denoise (DISTORTED->CLEAN) supervised by pairs of CLEAN and DISTORTED images. Regrettably, capturing DISTORTED sensor readings is time-consuming; as well, there is a lack of CLEAN HDR videos. We suggest a method to overcome those two limitations. First, we learn a different function instead: CLEAN->DISTORTED, which generates samples containing correlated pixel noise, and row and column noise, as well as motion blur from a low number of CLEAN sensor readings. Second, as there is not enough CLEAN HDR video available, we devise a method to learn from LDR video in-stead. Our approach compares favorably to several strong baselines, and can boost existing methods when they are re-trained on our data. Combined with spatial and temporal super-resolution, it enables applications such as re-lighting with low noise or blur.