Normal Fréchet Drift: Measuring Post-Training Departure from Pretrained Reference Manifold

Post-training can improve a generator’s reward while moving its outputs away from pretrained reference geometry. We distinguish this normal drift from tangential drift, which redistributes probability along the same reference manifold. We introduce Normal Fréchet Drift (NFD), the expected squared distance to a fixed reference set in a shared feature space. Its ideal value is zero for distributions confined to that set. To estimate NFD from finite pretrained samples, we construct bounded Multi-Patch reconstructions: local plane patches centered at sampled features, with finite radii that control extrapolation. We separate evaluation sampling variance from reconstruction bias and bound the bias through local coverage, curvature, tangent, and anchor errors. Controlled geometries validate the distinction between normal and tangential drift and reveal the reconstruction-resolution limit. On Stable Diffusion 3.5 Medium, FlowDPO exhibits the largest reconstruction-relative departure, with stable ordering across prompt splits, encoders, and reference refits. A FLUX.2 comparison extends the diagnostic to distillation. Blinded judgments on selected image pairs associate lower NFD with better visual quality. NFD measures geometric departure alongside distributional and perceptual evaluations.