Trend filtering proposed by Kim et. al. (2009), provides a computationally feasible tool for performing nonparametric regression resembling splines in the univariate setting. Wang et al. (2011) provided an extension from the univariate case to graphs with their proposed Graph Trend Filtering. In our work, we propose a continuous-space Bayesian version of Graph Trend Filtering. Aberg and Podgorski (2011) provide motivation for implementing non-stationary second order random fields with heavier tails to provide models with better flexibility. To provide a model that adapts better to local behavior, we propose a model that fits a spatial term to a Laplace Random Field. We illustrate the utility of this approach on a study of spatial disease mapping, where we show that our proposed approach is less prone to spatial confounding.