Large language models (LLMs)  often hallucinate and lack the ability to provide attribution for their generations. Semi-parametric LMs, such asNN-LM, approach these limitations by refining the output of an LM for a given prompt using its nearest neighbor matches in a non-parametric data store. However, these models often exhibit slow inference speeds and produce non-fluent texts. In this paper, we introduce Nearest Neighbor Speculative Decoding (Nest) , a novel semi-parametric language modeling approach that is capable of incorporating real-world text spans of arbitrary length into the LM generations and providing attribution to their sources.Nestperforms token-level retrieval at each inference step to compute a semi-parametric mixture distribution and identify promising span continuations in a corpus. It then uses an approximate speculative decoding procedure that accepts a prefix of the retrieved span or generates a new token.Nestsignificantly enhances the generation quality and attribution rate of the base LM across a variety of knowledge-intensive tasks, surpassing the conventionalNN-LM method and performing competitively with in-context retrieval augmentation. In addition,Nestsubstantially improves the generation speed, achieving a 1.8speedup in inference time when applied to Llama-2-Chat 70B.