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

• URL: http://arxiv.org/abs/2509.19903v1
• Date: Wed, 24 Sep 2025 08:57:21 GMT
• Title: Latent Iterative Refinement Flow: A Geometric-Constrained Approach for Few-Shot Generation
• Authors: Songtao Li, Zhenyu Liao, Tianqi Hou, Ting Gao,
• Abstract summary: We introduce Latent Iterative Refinement Flow (LIRF), a novel approach to few-shot generation.<n>LIRF establishes a stable latent space using an autoencoder trained with our novel textbfmanifold-preservation loss.<n>Within this cycle, candidate samples are refined by a geometric textbfcorrection operator, a provably contractive mapping.
• Score: 5.062604189239418
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Few-shot generation, the synthesis of high-quality and diverse samples from limited training data, remains a significant challenge in generative modeling. Existing methods trained from scratch often fail to overcome overfitting and mode collapse, and fine-tuning large models can inherit biases while neglecting the crucial geometric structure of the latent space. To address these limitations, we introduce Latent Iterative Refinement Flow (LIRF), a novel approach that reframes few-shot generation as the progressive densification of geometrically structured manifold. LIRF establishes a stable latent space using an autoencoder trained with our novel \textbf{manifold-preservation loss} $L_{\text{manifold}}$. This loss ensures that the latent space maintains the geometric and semantic correspondence of the input data. Building on this, we propose an iterative generate-correct-augment cycle. Within this cycle, candidate samples are refined by a geometric \textbf{correction operator}, a provably contractive mapping that pulls samples toward the data manifold while preserving diversity. We also provide the \textbf{Convergence Theorem} demonstrating a predictable decrease in Hausdorff distance between generated and true data manifold. We also demonstrate the framework's scalability by generating coherent, high-resolution images on AFHQ-Cat. Ablation studies confirm that both the manifold-preserving latent space and the contractive correction mechanism are critical components of this success. Ultimately, LIRF provides a solution for data-scarce generative modeling that is not only theoretically grounded but also highly effective in practice.

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