Generative Anchored Fields: Controlled Data Generation via Emergent Velocity Fields and Transport Algebra
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917275202748416 |
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| author | Deressa, Deressa Wodajo Mareen, Hannes Lambert, Peter Van Wallendael, Glenn |
| author_facet | Deressa, Deressa Wodajo Mareen, Hannes Lambert, Peter Van Wallendael, Glenn |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_22693 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generative Anchored Fields: Controlled Data Generation via Emergent Velocity Fields and Transport Algebra Deressa, Deressa Wodajo Mareen, Hannes Lambert, Peter Van Wallendael, Glenn Machine Learning 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. |
| title | Generative Anchored Fields: Controlled Data Generation via Emergent Velocity Fields and Transport Algebra |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2511.22693 |