Understanding human belief dynamics is a crucial problem for our society. Many different approaches have been used to understand and predict how individual beliefs form and spread. Some approaches investigate how social network mechanisms promote or impede spread of beliefs. Others focus on cognitive mechanisms underlying belief spread, including strategies for belief updating, network updating, and representation of social environments. We present a modular framework that integrates these different mechanisms using the theory of cognitive dissonance and the formalism of statistical physics models. The framework enables specifying and comparing different models of belief dynamics that have been so far studied independently. It can reproduce established empirical and theoretical findings about belief dynamics, and describe belief change in empirical data from longitudinal studies.