Despite progress in designing protein-binding proteins, the shape matching of designs to targets is lower than in many native protein complexes, and design efforts have failed for the tumor necrosis factor receptor 1 (TNFR1) and other protein targets with relatively flat and polar surfaces. We hypothesized that free diffusion from random noise could generate shape-matched binders for challenging targets and tested this approach on TNFR1. We obtain designs with low picomolar affinity whose specificity can be completely switched to other family members using partial diffusion. Designs function as antagonists or as superagonists when presented at higher valency for OX40 and 4-1BB. The ability to design high-affinity and high-specificity antagonists and agonists for pharmacologically important targets in silico presages a coming era in protein design in which binders are made by computation rather than immunization or random screening approaches.