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In contrast, multi-frame super-resolution (MFSR) offers the possibility of reconstructing rich details by combining signal information from multiple shifted images. This key advantage, along with the increasing popularity of burst photography, have made MFSR an important problem for real-world applications. We propose a novel architecture for the burst super-resolution task. Our network takes multiple noisy RAW images as input, and generates a denoised, super-resolved RGB image as output. This is achieved by explicitly aligning deep embeddings of the input frames using pixel-wise optical flow. The information from all frames are then adaptively merged using an attention-based fusion module. In order to enable training and evaluation on real-world data, we additionally introduce the BurstSR dataset, consisting of smartphone bursts and high-resolution DSLR ground-truth. 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