{"ID":2866458,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.19903","arxiv_id":"2509.19903","title":"Latent Iterative Refinement Flow: A Geometric Constrained Approach for Few-Shot Generation","abstract":"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.","short_abstract":"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...","url_abs":"https://arxiv.org/abs/2509.19903","url_pdf":"https://arxiv.org/pdf/2509.19903v2","authors":"[\"Songtao Li\",\"Tianqi Hou\",\"Zhenyu Liao\",\"Ting Gao\"]","published":"2025-09-24T08:57:21Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[\"Diffusion Model\"]","has_code":false}