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Speculative Decoding has two innovations: Spec-Drafter -- an independent model specially optimized for efficient and accurate drafting -- and Spec-Verification -- a reliable method for verifying the drafted tokens efficiently in the decoding paradigm. Experimental results on various seq2seq tasks including machine translation and abstractive summarization show our approach can achieve around $5\\times$ speedup for the popular Transformer architectures with comparable generation quality to beam search decoding, refreshing the impression that the draft-then-verify paradigm introduces only $1.4\\times$$\\sim$$2\\times$ speedup. In addition to the remarkable speedup, we also demonstrate 3 additional advantages of SpecDec, revealing its practical value for accelerating generative models in real-world applications. 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