We present a novel self-supervised framework for learning the discretization-agnostic surface parameterization of arbitrary 3D objects with both bounded and unbounded surfaces. Our framework leverages diffusion-enabled global-to-local shape context for each vertex first to partition the unbounded surface into multiple patches using the proposed self-supervised PatchNet and subsequently perform independent UV parameterization of these patches by learning forward and backward UV mapping for individual patches. Thus, our framework enables learning a discretization-agnostic parameterization at a lower resolution and then directly inferring the parameterization for a higher-resolution mesh without retraining. We evaluate our framework on multiple 3D objects from the publicly available SHREC [Lian et al. 2011] dataset and report superior/faster UV parameterization over conventional methods. © 2022 ACM.