Latent Iterative Refinement Flow: A Geometric Constrained Approach for Few-Shot Generation

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 velocity field collapse, where the learned field degenerates into isolated point attractors and trap the sampling trajectories. Inspired by this novel view, we introduce textbfBLUE Latent BLUE Iterative BLUE Refinement BLUE Flow (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 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.