# CurveFlow: Curvature-Guided Flow Matching for Image Generation Source: [CurveFlow: Curvature-Guided Flow Matching for Image Generation]() Collection index: [llms.txt]() Data updated: 2025-10-26T05:27:47.170Z Authors: Yan Luo, Drake Du, Hao Huang, Yi Fang, Mengyu Wang Published: 2025-08-20T22:06:13.000Z ## 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. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. ## Original sources and implementation [Original paper]() [PDF]()