Figure 2: Training and inference of S3-PnP. Purple arrows indicate full-space learning with P = 0,
s
P = I, and β = 0. Orange arrows indicate structure-guided learning: D is trained and frozen, and
g s s
its correction is enabled to collect a new state training set for D . At inference, active corrections are
g
evaluated at the same ADMM input and combined before a single analytical prior update. Snowflakes
denote frozen networks.