Abstract: We introduce a hierarchical generative representation for strand hair geometry that progresses from coarse, low-pass filtered guide strands to densely populated hair strands rich in high-frequency details. Unlike traditional methods that sample guide strands from a regular 2D grid on a UV scalp map, our model utilizes $k$-medoids clustering centers from low-pass filtered dense strands as guide curves, which more accurately retain the hairstyle's inherent characteristics. We employ the discrete cosine transform (DCT) to separate low-frequency structural curves from high-frequency curliness and noise, avoiding the Gibbs' oscillation issues associated with the standard Fourier transform in open curves. Our variational autoencoder-based model, with its permutation-equivariant architecture, facilitates flexible, off-the-grid guide strand geometry modeling and enables the completion of dense strands in any quantity and density, drawing on principles from implicit neural representations. Empirical evaluations confirm the capacity of the model to generate convincing guide curves and dense strands, complete with nuanced high-frequency details.