There has been a vast amount of discussion about the positive and negative regional effect on policy diffusion. During this debate, the role of neighborhood structure is ignored and the linear assumption is still prevailing in this field. By analyzing the spatial convergence of local vocational education development with data of 31 provinces from 1995 to 2008 in China, we explore the effects of neighborhood interactions on policy diffusion, paying specific attention to the dynamical role of neighborhood structures in policy diffusion. The empirical results clearly indicate that the development of local vocational education systems in China is spatially autocorrelated to the neighboring provinces. Local vocational education systems converge more slowly if a spatially lagged dependent variable is introduced, while they converge faster if a spatially error variable is introduced. The policy transition between neighbors considering their local spatial context is analyzed with Spatial Markov Chain and a fundamental nonlinear connection between neighborhood structure and policy transition is unveiled. Using spatial econometric models, we also find that the socio-spatial diffusion patterns with the social factors such as consumption, urban/rural distribution and occupation serve as barriers to and amplifiers of policy diffusion. These results not only resonate with conventional linear wisdom on policy diffusion but also offer a new nonlinear perspective on socio-spatial patterns of policy diffusion that are clearly embedded within the local neighborhood structures.