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Reference-based super-resolution (RefSR) has made significant progress in producing realistic textures using an external reference (Ref) image. However, existing RefSR methods obtain high-quality correspondence matchings consuming quadratic computation resources with respect to the input size, limiting its application. Moreover, these approaches usually suffer from scale misalignments between the low-resolution (LR) image and Ref image. In this paper, we propose an Accelerated Multi-Scale Aggregation network (AMSA) for Reference-based Super-Resolution, including Coarse-to-Fine Embedded PatchMatch (CFE-PatchMatch) and Multi-Scale Dynamic Aggregation (MSDA) module. To improve matching efficiency, we design a novel Embedded PatchMacth scheme with random samples propagation, which involves end-to-end training with asymptotic linear computational cost to the input size. To further reduce computational cost and speed up convergence, we apply the coarse-to-fine strategy on Embedded PatchMacth constituting CFE-PatchMatch. To fully leverage reference information across multiple scales and enhance robustness to scale misalignment, we develop the MSDA module consisting of Dynamic Aggregation and Multi-Scale Aggregation. The Dynamic Aggregation corrects minor scale misalignment by dynamically aggregating features, and the Multi-Scale Aggregation brings robustness to large scale misalignment by fusing multi-scale information. Experimental results show that the proposed AMSA achieves superior performance over state-of-the-art approaches on both quantitative and qualitative evaluations.