Generative Anchored Fields: Controlled Data Generation via Emergent Velocity Fields and Transport Algebra
This work addresses the need for more flexible and controllable generative models in machine learning, offering a novel architectural approach for tasks like interpolation and semantic editing.
The paper tackles the problem of controllable data generation by introducing Generative Anchored Fields (GAF), which learns independent endpoint predictors to enable compositional control via transport algebra, achieving strong sample quality with FID scores of 7.51 on ImageNet 256x256 and 7.27 on CelebA-HQ 256x256.
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.