CoreFlow: Low-Rank Matrix Generative Models

CoreFlow, introduced by Dongze Wu, Linglingzhi Zhu, and Yao Xie, tackles the challenge of learning matrix-valued distributions from high-dimensional, often incomplete training data. Traditional ambient-space generative models are computationally expensive and statistically fragile when matrix dimensions are large but sample sizes are limited. CoreFlow is a geometry-preserving low-rank flow model that first learns shared row and column subspaces across the matrix distribution, then trains a continuous normalizing flow only on the induced low-dimensional core. This approach separates shared matrix geometry from sample-specific variation, preserving matrix structure and substantially improving training efficiency.

CoreFlow also handles incomplete training matrices through masked Riemannian updates and iterative completion. Across real and synthetic benchmarks, it substantially improves spectral and moment-level generation quality in few-sample regimes while remaining competitive in data-rich settings, even when compressed to 9% of the ambient dimension and with up to 40% missing training entries. This makes CoreFlow particularly valuable for high-dimensional, limited-sample applications like medical imaging, genomics, or any domain where collecting large, complete matrix datasets is infeasible.