Critical Boundary Detector (CBD)

methods / Theoretical / Analytical / Geometric analysis / Critical Boundary Detector (CBD)

Techniqueadvanced

Computes the Frobenius norm of the Jacobian of a diffusion model's own normalized score/velocity field at a point along a single generation trajectory, using local spikes in this quantity to flag branch-sensitive 'switching bands' where the generative trajectory is about to commit to one of several competing denoising outcomes.

Used in (1 observation)

A real DDPM's Critical Boundary Detector correlates with LPIPS and localizes classifier-guidance-worthy timestepsmeasured

structure: Curvature profile of the representation manifold · models: DDPM (CIFAR-10, unconditional), Stable Diffusion 3.5 Medium · paper: The Geometry of Phase Transitions in Generative Dynamics via Projection Caustics