Lightweight material capture methods require a material prior, defining the subspace of plausible textures within the large space of unconstrained texel grids. Previous work has either used deep neural networks (trained on large synthetic material datasets) or procedural node graphs (constructed by expert artists) as such priors. In this paper, we propose a semi-procedural differentiable material prior that represents materials as a set of (typically procedural) grayscale noises and patterns that are processed by a sequence of lightweight learnable convolutional filter operations. We demonstrate that the restricted structure of this architecture acts as an inductive bias on the space of material appearances, allowing us to optimize the weights of the convolutions per-material, with no need for pre-training on a large dataset. Combined with a differentiable rendering step and a perceptual loss, we enable single-image tileable material capture comparable with state of the art. Our approach does not target the pixel-perfect recovery of the material, but rather uses noises and patterns as input to match the target appearance. To achieve this, it does not require complex procedural graphs, and has a much lower complexity, computational cost and storage cost. We also enable control over the results, through changing the provided patterns and using guide maps to push the material properties towards a user-driven objective.