{"ID":2880426,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.15093","arxiv_id":"2508.15093","title":"CurveFlow: Curvature-Guided Flow Matching for Image Generation","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.","short_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 t...","url_abs":"https://arxiv.org/abs/2508.15093","url_pdf":"https://arxiv.org/pdf/2508.15093v2","authors":"[\"Yan Luo\",\"Drake Du\",\"Hao Huang\",\"Yi Fang\",\"Mengyu Wang\"]","published":"2025-08-20T22:06:13Z","proceeding":"cs.CV","tasks":"[\"cs.CV\"]","methods":"[\"Diffusion Model\"]","has_code":false,"code_links":[{"ID":610674,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_id":2880426,"paper_url":"https://arxiv.org/abs/2508.15093","paper_title":"CurveFlow: Curvature-Guided Flow Matching for Image Generation","repo_url":"https://github.com/Harvard-AI-and-Robotics-Lab/CurveFlow","is_official":false,"mentioned_in_paper":false,"mentioned_in_github":true,"github_stars":0}]}