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

2025-11-27

AI Summary

This work addresses two key limitations in controllable generation: the complexity of trajectory modeling and coarse-grained control. To this end, we propose the Generative Anchoring Field (GAF), which abandons conventional trajectory prediction and instead learns two independent endpoint predictors— a noise-endpoint predictor $J$ and a data-endpoint predictor $K$—such that the velocity field $v = K - J$ emerges naturally, enabling decoupled and composable generation control. We introduce Transport Algebra, elevating compositional operations—including cross-modal semantic interpolation, hybrid generation, and morphological deformation—to first-class architectural primitives. Furthermore, GAF employs class-specific $K_n$ heads jointly with a shared base distribution for improved modeling fidelity. Evaluated on CelebA-HQ, GAF achieves an FID of 7.5 and enables lossless cyclic transport (LPIPS ≈ 0.0), demonstrating significant improvements in both generation quality and fine-grained controllability.

Technology Category

• Natural Language Processing: Generation
• Computer Vision: Generative Adversarial Networks (GANs) for Vision
• Machine Learning: Deep Generative Models & Autoencoders

Application Category

• Social Networks and Social Media: Generative AI / large language models and their impact on social systems
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications

Abstract

We present Generative Anchored Fields (GAF), a generative model that learns independent endpoint predictors $J$ (noise) and $K$ (data) rather than a trajectory predictor. The velocity field $v=K-J$ emerges from their time-conditioned disagreement. This factorization enables extit{Transport Algebra}: algebraic operation on learned ${(J_n,K_n)}_{n=1}^N$ heads for compositional control. With class-specific $K_n$ heads, GAF supports a rich family of directed transport maps between a shared base distribution and multiple modalities, enabling controllable interpolation, hybrid generation, and semantic morphing through vector arithmetic. We achieve strong sample quality (FID 7.5 on CelebA-HQ $64 imes 64$) while uniquely providing compositional generation as an architectural primitive. We further demonstrate, GAF has lossless cyclic transport between its initial and final state with LPIPS=$0.0$. Code available at https://github.com/IDLabMedia/GAF

Problem

• Generates controlled data via emergent velocity fields
• Enables compositional control through transport algebra
• Supports directed transport between shared base and modalities

Innovation

• Learns independent endpoint predictors J and K
• Velocity field emerges from their time-conditioned disagreement
• Enables compositional control via Transport Algebra operations