CoreFlow: Low-Rank Matrix Generative Models

Learning matrix-valued distributions from high-dimensional and possibly incomplete training data is challenging: ambient-space generative modeling is computationally expensive and statistically fragile when the matrix dimension is large but the number of training samples is limited. We propose \emph{CoreFlow}, a two-stage generative framework that first learns shared low-rank geometry and then trains an expressive continuous normalizing flow only in the induced low-dimensional core space. The model preserves matrix structure, handles incomplete training matrices through masked Riemannian updates and iterative completion, and substantially improves training efficiency. Across real and synthetic benchmarks, CoreFlow improves spectral and moment-level generation quality, even under compression to $9\%$ of the ambient dimension on real data and with up to $40\%$ missing entries in the training matrices.