We present Diff3F as a simple, robust, and class-agnostic feature descriptor that can be computed for untextured input shapes (meshes or point clouds). Our method distills diffusion features from image foundational models onto input shapes. Specifically, we use the input shapes to produce depth and normal maps as guidance for conditional image synthesis, and in the process produce (diffusion) features in 2D that we subsequently lift and aggregate on the original surface. Our key observation is that even if the conditional image generations obtained from multi-view rendering of the input shapes are inconsistent, the associated image features are robust and can be directly aggregated across views. This produces semantic features on the input shapes, without requiring additional data or training. We perform extensive experiments on multiple benchmarks (SHREC'19, SHREC'20, and TOSCA) and demonstrate that our features, being semantic instead of geometric, produce reliable correspondence across both isometeric and non-isometrically related shape families.