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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.19903 |
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Table of Contents:
- Diffusion and flow-matching models trained with limited data often tend to memorize the training data instead of generalization, leading to severely reduced diversity. In this paper, we provide a dynamical perspective and identify this ``collapse-to-memorization'' phenomenon as a consequence of the \emph{velocity field collapse}, where the learned field degenerates into isolated point attractors and trap the sampling trajectories. Inspired by this novel view, we introduce \textbf{{\BLUE L}atent {\BLUE I}terative {\BLUE R}efinement {\BLUE F}low ({\BLUE LIRF})}, a geometry-aware framework for from-scratch training of diffusion models in the limited-data regime. By exploiting the intrinsic geometry of a semantically aligned latent space, LIRF progressively densifies the training data manifold via a \emph{generation--correction--augmentation} closed loop, thereby effectively resolving the velocity field collapse. Theoretical guarantee on the convergence of this manifold densification procedure is also provided. Experiments on FFHQ subsets and Low-Shot datasets demonstrate the advantageous performance of LIRF over existing diffusion models for limited-data generation, achieving significantly higher diversity and recall, with comparably good generative performance.