# Generative Anchored Fields: Controlled Data Generation via Emergent Velocity Fields and Transport Algebra

Source: [Generative Anchored Fields: Controlled Data Generation via Emergent Velocity Fields and Transport Algebra](<https://www.sota2.com/research/paper/692d2155d6b0dd33429319dd>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-02-18T05:00:15.522Z

Authors: Deressa Wodajo Deressa, Hannes Mareen, Peter Lambert, Glenn Van Wallendael

Published: 2025-11-27T18:48:42.000Z

## 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.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Image Generation on CelebA-HQ 256x256 (test)](<https://www.sota2.com/research/sota/image-generation-on-celeba-hq-256x256-test.md>): Image Generation; CelebA-HQ 256x256 (test); FID: 10.32.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2511.22693>)

[PDF](<https://arxiv.org/pdf/2511.22693.pdf>)