Consensus Matryoshka: Laplacian-Cost OT Flows for Multi-Scale Inpainting

Minibatch OT-CFM shortens unconditional interpolants, but a Euclidean plan on whole images is the wrong coupling for inpainting: it can match one observation's border to another image' s interior, and a fresh plan at each pyramid scale is not the downsample of one displacement field. 39 We keep OT, but change the \emph{cost} and the \emph{feasible set}. 40 \textbf{Consensus Matryoshka} computes a \emph{single} minibatch plan whose cost is a weighted Laplacian pyramid of the \emph{holes}, then builds a chimeric target that freezes known p ixels. 41 The resulting velocity $u$ is itself Laplacian-factored so nested U-Nets predict low-pass motion and band-pass residuals of that same field. 42 Capacity is Matryoshka: a deep, attentive coarse branch models principal hole motion; the $256^2$ head is a light convolutional residual. 43 On CelebA-HQ center-hole inpainting, an $83$M model at $40$k steps and $10$ Euler steps attains FID $7.69$ vs.\ $9.02$ for a $91$M PixelFlow cascade, remaining stable at $40$ steps (FI D $8.19$ vs.\ $12.61$).