{"ID":2836096,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.22693","arxiv_id":"2511.22693","title":"Generative Anchored Fields: Controlled Data Generation via Emergent Velocity Fields and Transport Algebra","abstract":"We present Generative Anchored Fields (GAF), a generative model that learns independent endpoint predictors, $J$ (noise) and $K$ (data), from any point on a linear bridge. Unlike existing approaches that use a single trajectory or score predictor, GAF is trained to recover the bridge endpoints directly via coordinate learning. The velocity field $v=K-J$ emerges from their time-conditioned disagreement. This factorization enables \\textit{Transport Algebra}: algebraic operations on multiple $J/K$ heads for compositional control. With class-specific $K_n$ heads, GAF defines directed transport maps between a shared base noise distribution and multiple data domains, allowing controllable interpolation, multi-class composition, and semantic editing. This is achieved either directly on the predicted data coordinates ($K$) using Iterative Endpoint Refinement (IER), a novel sampler that achieves high-quality generation in $5-8$ steps, or on the emergent velocity field ($v$). We achieve strong sample quality (FID 7.51 on ImageNet $256\\times256$ and $7.27$ on CelebA-HQ $256\\times 256$, without classifier-free guidance) while treating compositional generation as an architectural primitive. Code available at https://github.com/IDLabMedia/GAF.","short_abstract":"We present Generative Anchored Fields (GAF), a generative model that learns independent endpoint predictors, $J$ (noise) and $K$ (data), from any point on a linear bridge. Unlike existing approaches that use a single trajectory or score predictor, GAF is trained to recover the bridge endpoints directly via coordinate l...","url_abs":"https://arxiv.org/abs/2511.22693","url_pdf":"https://arxiv.org/pdf/2511.22693v2","authors":"[\"Deressa Wodajo Deressa\",\"Hannes Mareen\",\"Peter Lambert\",\"Glenn Van Wallendael\"]","published":"2025-11-27T18:48:42Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[]","has_code":false,"code_links":[{"ID":606571,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_id":2836096,"paper_url":"https://arxiv.org/abs/2511.22693","paper_title":"Generative Anchored Fields: Controlled Data Generation via Emergent Velocity Fields and Transport Algebra","repo_url":"https://github.com/IDLabMedia/GAF","is_official":false,"mentioned_in_paper":false,"mentioned_in_github":true,"github_stars":0}]}