This work presents a geometry-aware approach to heterogeneous single-particle cryo-EM reconstruction that predicts atomic backbone conformations. It represents the protein backbone as a graph and uses a graph neural network autodecoder to map per-image latent variables to three-dimensional displacements of a template conformation. The objective combines a differentiable cryo-EM forward model with geometric regularization and supports unknown orientations through ellipsoidal support lifting. On synthetic datasets from molecular dynamics trajectories, the GNN improves over a comparable multilayer perceptron, illustrating the value of protein-structure priors.