Generative Anchored Fields: Endpoint Learning for Generative Modeling

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. Instead of learning the local path along a trajectory, as in diffusion or flow-based models, GAF is trained to identify the endpoint coordinates of a bridge state directly via an endpoint regression objective. Central to our approach is the decoupling of time-dependent feature learning from endpoint prediction. Unlike the transport-based models that learn a monolithic time-conditioned predictor that maps noise to data via a unified field, GAF uses a shared trunk, \(\Phi\), which produces a time-conditioned feature bank and a pair of linear predictors, \(J\) and \(K\). This separation of feature learning from prediction enables \textit{Transport Algebra}: algebraic operations on multiple \(J\) and \(K\) heads for compositional sampling. Additionally, with class-specific \(K_n\) heads, where \(n\in\{1,...,N\}\) for \(N\) classes, 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 (i) Iterative Endpoint Refinement (IER), a novel sampler that achieves high-quality generation in \(5-8\) forward steps, or (ii) on the derived velocity field \(v=K-J\). GAF achieves strong sample quality with an FID of 2.25 on ImageNet \(256\times256\) while treating compositional generation as an architectural primitive. Code available at this https URL

Machine Learning (cs.LG)

arXiv:2511.22693 [cs.LG]

(or arXiv:2511.22693v3 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2511.22693 Focus to learn more arXiv-issued DOI via DataCite

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