Generative Anchored Fields: Controlled Data Generation via Emergent Velocity Fields and Transport Algebra (GAF)
Modern generative models achieve remarkable sample quality but lack precise compositional control, the ability to independently manipulate, interpolate, or combine learned representations at inference time. Current approaches treat control as an external steering process through classifier-free guidance, prompt engineering, or attention manipulation, rather than an intrinsic property of the learned representation. This raises a fundamental question: must we learn a step-by-step mechanism of the trajectory, or is it sufficient to know only its origin and destination?
We present Generative Anchored Fields (GAF), where generation is an explicit algebraic operation. Rather than learning a single trajectory predictor, GAF learns independent endpoint operators: J anchored to noise, K anchored to data, with velocity emerging naturally as v = K − J. This simple factorization unlocks Transport Algebra: switch between K heads mid-trajectory, interpolate between class manifolds, or arithmetically combine predictors for novel outputs.
GAF supports three inference modes from a single model. 1. ODE integration, 2. Iterative Endpoint Refinement (IER) in 5–8 steps, and 3. hybrid switching between them. GAF achieves FID 7.51 on ImageNet 256×256 without classifier-free guidance.
Read the full paper ArXiv paper link
Code available at: GAF github link
