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

arXiv: https://arxiv.org/abs/2509.19903 · HTML: https://mlsanity.com/paper/2509.19903/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 41 of its 54 references that are in the map.
- First posted on arXiv 24 Sep 2025.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 30 of 41)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [DreamBooth: Fine Tuning Text-to-Image Diffusion Models for Subject-Driven Generation](https://mlsanity.com/paper/2208.12242/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Training Generative Adversarial Networks with Limited Data](https://mlsanity.com/paper/2006.06676/) (2020)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [FLUX.1 Kontext: Flow Matching for In-Context Image Generation and Editing in Latent Space](https://mlsanity.com/paper/2506.15742/) (2025)
- [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Extracting Training Data from Diffusion Models](https://mlsanity.com/paper/2301.13188/) (2023)
- [Interpreting the Latent Space of GANs for Semantic Face Editing](https://mlsanity.com/paper/1907.10786/) (2019)
- [Diffusion Art or Digital Forgery? Investigating Data Replication in Diffusion Models](https://mlsanity.com/paper/2212.03860/) (2022)
- [Differentiable Augmentation for Data-Efficient GAN Training](https://mlsanity.com/paper/2006.10738/) (2020)
- [Generalization in diffusion models arises from geometry-adaptive harmonic representations](https://mlsanity.com/paper/2310.02557/) (2023)
- [Open-Sora 2.0: Training a Commercial-Level Video Generation Model in 200k](https://mlsanity.com/paper/2503.09642/) (2025)
- [Flow Matching in Latent Space](https://mlsanity.com/paper/2307.08698/) (2023)
- [Patch Diffusion: Faster and More Data-Efficient Training of Diffusion Models](https://mlsanity.com/paper/2304.12526/) (2023)
- [On Memorization in Diffusion Models](https://mlsanity.com/paper/2310.02664/) (2023)
- [Deep Feature Interpolation for Image Content Changes](https://mlsanity.com/paper/1611.05507/) (2016)

## Abstract (arXiv)

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.