Generative Anchored Fields: Endpoint Learning for Generative Modeling

arXiv:2511.22693v3 Announce Type: replace 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 https://github.com/IDLabMedia/GAF