Policy diffusion occurs when policies in one unit (e.g., countries, states, cities) are influenced by the prior adoption of policies in other units. Although numerous studies have convincingly documented this phenomenon, they have, with very few exceptions, generally ignored a crucial step in the diffusion process—namely, how policies are framed ahead of their adoption. Policy frames—the discussion of a policy from particular viewpoints—play a crucial role in linking the actions of previous units with the potential actions in other units. In this paper, we identify policy frames and examine their link with prior policy adoptions. We focus on the area of restrictions on smoking in U.S. states. Our analysis draws upon an original dataset of more than four million paragraphs from articles published in 50 American newspapers covering 47 states between 1996 and 2014. We use structural topic models to estimate how smoking bans have been framed and how frames change as a function of policy adoption in other states. We find that, as more neighboring states enact legislation restricting smoking, concerns about the restaurant business decrease; worries about the casino business increase; detailed regulations such as ventilation requirements or separate rooms for smokers are discussed less frequently; voters’ support and involvement in the decision-making process surrounding smoking bans are discussed more frequently; the compatibility of smoking restrictions with individual rights loses salience as a topic; and the passage of legislation is discussed more frequently, while the process by which decisions are made loses salience. These findings establish a foothold for the usefulness of structural topic models and support for the idea that policy frames are an important part of the diffusion process.