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

2025-09-24

AI Summary

Few-shot generative modeling suffers from overfitting and mode collapse, and existing approaches struggle to jointly preserve latent-space geometric structure and ensure high-fidelity generation. To address this, we propose a “Generate–Correct–Enhance” iterative framework. First, we introduce a manifold-preserving loss to construct a semantically consistent latent manifold. Second, we design a geometric correction operator based on contraction mapping, which theoretically guarantees monotonic reduction of the Hausdorff distance between the generated and true data manifolds. Third, we integrate iterative refinement with structural-aware data augmentation to enable geometry-informed sample evolution. Evaluated on benchmarks including AFHQ-Cat, our method generates high-resolution, high-fidelity, and diverse images, substantially outperforming state-of-the-art few-shot generative models. Ablation studies confirm the critical contribution of each component.

Technology Category

• Computer Vision: Generative Adversarial Networks (GANs) for Vision
• Machine Learning: Learning with Manifolds
• Natural Language Processing: Generation

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications

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 extbf{manifold-preservation loss} $L_{ ext{manifold}}$. 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 extbf{correction operator}, a provably contractive mapping that pulls samples toward the data manifold while preserving diversity. We also provide the extbf{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.

Problem

• Overcoming overfitting and mode collapse in few-shot generation from limited data
• Addressing geometric structure neglect in latent space during fine-tuning
• Progressive densification of geometrically structured manifold for data-scarce generation

Innovation

• Manifold-preservation loss maintains geometric latent structure
• Iterative correction operator contracts samples toward manifold
• Convergence Theorem guarantees decreasing Hausdorff distance