Method
F2D-Net addresses two failure modes of all-in-one restorers on composite inputs: deterministic flow transport collapses to the conditional mean, and image-level expert routing leaves experts under-specialized.
Figure 1. Overview of F2D-Net. The restoration velocity field is factorized into a shared backbone and four degradation-specific expert increments, assembled at every pixel via learned spatial gating maps and time-conditioned coefficients.
Stochastic transport with state-dependent noise. We formulate restoration as a forward-only stochastic transport process from the degraded observation to the clean target. The diffusion coefficient is scaled by the residual to the target, so the noise is large far from the solution and contracts to zero upon convergence:
This SDE admits a closed-form log-normal transition, which enables direct sampling of intermediate states during training and reduces inference to a single network evaluation through analytic transitions.
Factorized velocity field. Vector additivity of flow matching motivates decomposing the restoration velocity into a shared backbone and degradation-specific expert increments, assembled at every pixel through spatial intensity maps mi and time-conditioned gating weights αi:
A lightweight CNN parser produces both the spatial maps mi and the global degradation weights w in one forward pass; the time-conditioned gate then schedules each expert across the transport trajectory. The shared backbone absorbs cross-degradation interactions while each Δfi specializes on a single atomic flow.
