CurveFlow: Curvature-Guided Flow Matching for Image Generation

• URL: http://arxiv.org/abs/2508.15093v2
• Date: Sun, 24 Aug 2025 04:41:55 GMT
• Title: CurveFlow: Curvature-Guided Flow Matching for Image Generation
• Authors: Yan Luo, Drake Du, Hao Huang, Yi Fang, Mengyu Wang,
• Abstract summary: Existing rectified flow models are based on linear trajectories between data and noise distributions.<n>This linearity enforces zero curvature, which can inadvertently force the image generation process through low-probability regions of the data manifold.<n>We introduce CurveFlow, a novel flow matching framework designed to learn smooth, non-linear trajectories by incorporating curvature guidance into the flow path.
• Score: 11.836900973675297
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Existing rectified flow models are based on linear trajectories between data and noise distributions. This linearity enforces zero curvature, which can inadvertently force the image generation process through low-probability regions of the data manifold. A key question remains underexplored: how does the curvature of these trajectories correlate with the semantic alignment between generated images and their corresponding captions, i.e., instructional compliance? To address this, we introduce CurveFlow, a novel flow matching framework designed to learn smooth, non-linear trajectories by directly incorporating curvature guidance into the flow path. Our method features a robust curvature regularization technique that penalizes abrupt changes in the trajectory's intrinsic dynamics.Extensive experiments on MS COCO 2014 and 2017 demonstrate that CurveFlow achieves state-of-the-art performance in text-to-image generation, significantly outperforming both standard rectified flow variants and other non-linear baselines like Rectified Diffusion. The improvements are especially evident in semantic consistency metrics such as BLEU, METEOR, ROUGE, and CLAIR. This confirms that our curvature-aware modeling substantially enhances the model's ability to faithfully follow complex instructions while simultaneously maintaining high image quality. The code is made publicly available at https://github.com/Harvard-AI-and-Robotics-Lab/CurveFlow.

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