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Shape priors have long been known to be effective when reconstructing 3D shapes from noisy or incomplete data. When using a deep-learning based shape representation, this often involves learning a latent representation, which can be either in the form of a single global vector or of multiple local ones. The latter allows more flexibility but is prone to overfitting. In this paper, we advocate a hybrid approach representing shapes in terms of 3D meshes with a separate latent vector at each vertex. During training the latent vectors are constrained to have the same value, which avoids overfitting. For inference, the latent vectors are updated independently while imposing spatial regularization constraints. We show that this gives us both flexibility and generalization capabilities, which we demonstrate on several medical image processing tasks.