Although social scientists have long been interested in the process through which ideas and behavior diffuse, the identification of causal diffusion effects, also known as peer effects, remains challenging. Many scholars consider the commonly used assumption of no omitted confounders to be untenable due to contextual confounding and homophily bias. To address this long-standing identification problem, I introduce a class of stationary causal directed acyclic graphs (DAGs), which represent the time-invariant nonparametric causal structure. I first show that this stationary causal DAG implies a new statistical test that can detect a wide range of biases, including the two types mentioned above. The proposed test allows researchers to empirically assess the contentious assumption of no omitted confounders. In addition, I develop a difference-in-difference style estimator that can directly correct biases under an additional parametric assumption. Leveraging the proposed methods, I study the spatial diffusion of hate crimes in Germany. After correcting large upward bias in existing studies, I find hate crimes diffuse only to areas that have a high proportion of school dropouts. To highlight the general applicability of the proposed approach, I also analyze the network diffusion of human rights norms. The proposed methodology is implemented in a forthcoming open source software package.