This project investigates posterior sampling for linear inverse problems using a specific class of simple interpretable priors. We focus on energy-based models defined by the sum of learnable potential functions applied to linear filter responses. While these architectures are typically optimized for deterministic variational reconstruction, this work repurposes them for Bayesian uncertainty quantification. The goal is to implement and analyze sampling algorithms such as the (annealed) Metropolis adjusted Langevin algorithm on these models.