{"ID":5551798,"CreatedAt":"2026-07-02T01:54:51.863792489Z","UpdatedAt":"2026-07-04T08:49:21.884923308Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.00647","arxiv_id":"2607.00647","title":"Not All Prediction Targets Keep Training-Free Diffusion Guidance on the Manifold","abstract":"Training-free guidance (TFG) steers a pretrained diffusion model toward a desired attribute at inference. To be effective, this guidance must be applied from the earliest, high-noise steps of sampling. Because its objective (a classifier or energy) is defined on clean images, $ε$- and $v$-prediction models must first estimate the clean image $\\hat{x}$ from the noisy state at each step, and the accuracy of that estimate determines how easily guidance drifts off the data manifold. $x$-prediction, a recent alternative, outputs the clean image directly, removing this source of error even at high noise. This is our motivation. We provide a theoretical analysis of how each prediction target shapes this accuracy, and introduce guided-class FID (Child FID), a metric that exposes the manifold damage standard evaluation misses. Experiments on a new fine-grained bird benchmark and on style transfer confirm that $x$-prediction keeps guided samples on the manifold most reliably, making it the strongest foundation for training-free guidance. Code is available at https://github.com/ManLuML/on-manifold-tfg","short_abstract":"Training-free guidance (TFG) steers a pretrained diffusion model toward a desired attribute at inference. To be effective, this guidance must be applied from the earliest, high-noise steps of sampling. Because its objective (a classifier or energy) is defined on clean images, $ε$- and $v$-prediction models must first e...","url_abs":"https://arxiv.org/abs/2607.00647","url_pdf":"https://arxiv.org/pdf/2607.00647v1","authors":"[\"Yunsung Lee\",\"Hyeongmin Lee\"]","published":"2026-07-01T09:01:13Z","proceeding":"cs.CV","tasks":"[\"cs.CV\"]","methods":"[\"Diffusion Model\"]","has_code":false,"code_links":[{"ID":613845,"CreatedAt":"2026-07-02T01:54:51.863792489Z","UpdatedAt":"2026-07-02T01:54:51.863792489Z","DeletedAt":null,"paper_id":5551798,"paper_url":"https://arxiv.org/abs/2607.00647","paper_title":"Not All Prediction Targets Keep Training-Free Diffusion Guidance on the Manifold","repo_url":"https://github.com/ManLuML/on-manifold-tfg","is_official":false,"mentioned_in_paper":false,"mentioned_in_github":true,"github_stars":0}]}