# CoreFlow: Low-Rank Matrix Generative Models

arXiv: https://arxiv.org/abs/2604.24959 · HTML: https://mlsanity.com/paper/2604.24959/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 45 references that are in the map.
- First posted on arXiv 27 Apr 2026.

## Builds on (most cited first, 24 of 24)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [An Introduction to Matrix Concentration Inequalities](https://mlsanity.com/paper/1501.01571/) (2015)
- [Diffusion Transformers with Representation Autoencoders](https://mlsanity.com/paper/2510.11690/) (2025)
- [Nonconvex Optimization Meets Low-Rank Matrix Factorization: An Overview](https://mlsanity.com/paper/1809.09573/) (2018)
- [Diffusion models for missing value imputation in tabular data](https://mlsanity.com/paper/2210.17128/) (2022)
- [Diffusion Models for Time Series Applications: A Survey](https://mlsanity.com/paper/2305.00624/) (2023)
- [MissDiff: Training Diffusion Models on Tabular Data with Missing Values](https://mlsanity.com/paper/2307.00467/) (2023)
- [MCFlow: Monte Carlo Flow Models for Data Imputation](https://mlsanity.com/paper/2003.12628/) (2020)
- [Low Rank Matrix Completion via Robust Alternating Minimization in Nearly Linear Time](https://mlsanity.com/paper/2302.11068/) (2023)
- [Liouville Flow Importance Sampler](https://mlsanity.com/paper/2405.06672/) (2024)
- [DiffPuter: Empowering Diffusion Models for Missing Data Imputation](https://mlsanity.com/paper/2405.20690/) (2024)
- [Annealing Flow Generative Models Towards Sampling High-Dimensional and Multi-Modal Distributions](https://mlsanity.com/paper/2409.20547/) (2024)
- [Bayesian Uncertainty Quantification for Low-Rank Matrix Completion](https://mlsanity.com/paper/2101.01299/) (2021)
- [Local Flow Matching Generative Models](https://mlsanity.com/paper/2410.02548/) (2024)
- [DoFlow: Flow-based Generative Models for Interventional and Counterfactual Forecasting on Time Series](https://mlsanity.com/paper/2511.02137/) (2025)
- [Information-Guided Sampling for Low-Rank Matrix Completion](https://mlsanity.com/paper/1706.08037/) (2017)
- [Inference for Low-rank Completion without Sample Splitting with Application to Treatment Effect Estimation](https://mlsanity.com/paper/2307.16370/) (2023)

## Built on by (most cited first, 1 of 1)

- [GazeDiT: Gaze-Accurate Diffusion Image Generation for Eye Tracking via Spatial Conditioning](https://mlsanity.com/paper/2609.17814/) (2026)

## Abstract (arXiv)

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.