Digital media animation can better promote folk culture inheritance and innovation, and at the same time, folk culture also provides rich inspiration materials and cultural elements for the creation of digital media animation. In this paper, the mathematical structure of the threshold regression model is first sorted out, and the parameters of the model are estimated by using the search method and the smooth least squares method. Secondly, it analyzes the promotion effect of digital media animation on the dissemination of folk culture, takes the 2D animated short film “Red Bank” as a research example, and designs a questionnaire to obtain the research data. Finally, the benchmark regression model and threshold regression model were established with folk culture dissemination as the dependent variable, and benchmark regression, robustness test, and threshold effect verification were conducted. The results show that the audiovisual language, creation method, and display medium of digital media animation are significantly correlated with folk culture dissemination at 1% level, and its R2 fit value reaches 0.7439. The level of development of digital media technology has an obvious double-threshold effect on the dissemination of folk culture, and its double-threshold value is 1.028 and 2.251 respectively. Digital media animation can enhance the dissemination medium of folk culture, expand the dissemination medium, and improve the quality of folk culture. Communication media and enhance the influence of folk culture.