We analyze and extend a recently proposed model of linguistic diffusion in social networks, to analytically derive time to convergence, and to account for the innovation phase of lexical dynamics in networks. Our new model, the degree-biased voter model with innovation, shows that the probability of existence of a norm is inversely related to innovation probability. When the innovation rate in the population is low, variants that become norms are due to a peripheral member with high probability. As the innovation rate increases, the fraction of time that the norm is a peripheral-introduced variant and the total time for which a norm exists at all in the population decrease. These results align with historical observations of rapid increase and generalization of slang words, technical terms, and new common expressions at times of cultural change in some languages.