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CoreFlow learns matrix-valued distributions by identifying shared row/column subspaces and training a continuous normalizing flow on the low-dimensional "core" induced by these subspaces. This approach explicitly separates shared matrix geometry from sample-specific variation, leading to improved training efficiency and sample quality, especially in high-dimensional, limited-sample scenarios. Experiments on real and synthetic data demonstrate that CoreFlow achieves superior spectral and moment-level generation quality, even with significant data compression and missing entries.
Learning generative models for high-dimensional matrices doesn't have to be a computational nightmare: CoreFlow achieves state-of-the-art results in low-data regimes by learning shared low-rank structure.
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 sample size is limited. We propose CoreFlow, a geometry-preserving low-rank flow model that learns shared row/column subspaces across the matrix distribution, and then trains a continuous normalizing flow only on the induced low-dimensional core. CoreFlow is designed for settings where shared low-rank matrix geometry is present, especially in high-dimensional limited-sample regimes. This separates shared matrix geometry from sample-specific variation, preserves matrix structure, and substantially improves training efficiency. The same framework also handles incomplete training matrices through masked Riemannian updates and iterative completion. Across real and synthetic benchmarks, CoreFlow substantially improves spectral and moment-level generation quality in few-sample regimes while remaining competitive in data-rich settings, even under compression to 9% of the ambient dimension and with up to 40% missing training entries.
