We report the crystal structures and magnetic properties of two pseudopolymorphs of the S=1/2 Ti³⁺ coordination framework, KTi(C₂O₄)₂⋅xH₂O. Single-crystal x-ray and powder neutron diffraction measurements on α−KTi(C₂O₄)₂⋅xH₂O confirm its structure in the tetragonal I4/mcm space group with a square planar arrangement of Ti³⁺ ions. Magnetometry and specific heat measurements reveal weak antiferromagnetic interactions, with J₁≈7 K and J₂/J₁=0.11 indicating a slight frustration of nearest- and next-nearest-neighbor interactions. Below 1.8 K, α−KTi(C₂O₄)₂⋅xH₂O undergoes a transition to G-type antiferromagnetic order with magnetic moments aligned along the c axis of the tetragonal structure. The estimated ordered moment of Ti³⁺ in α−KTi(C₂O₄)₂⋅xH₂O is suppressed from its spin-only value to 0.62(3) μ_B, thus verifying the two-dimensional nature of the magnetic interactions within the system. β−KTi(C₂O₄)₂⋅2H₂O, on the other hand, realizes a three-dimensional diamondlike magnetic network of Ti³⁺ moments within a hexagonal P6₂22 structure. An antiferromagnetic exchange coupling of J≈54 K—an order of magnitude larger than in α−KTi(C₂O₄)₂⋅xH₂O—is extracted from magnetometry and specific heat data. β−KTi(C2O4)2⋅2H2O undergoes Néel ordering at TN=28 K, with the magnetic moments aligned within the ab plane and a slightly reduced ordered moment of 0.79 μ_B per Ti³⁺. Through density-functional theory calculations, we address the origin of the large difference in the exchange parameters between the α and β pseudopolymorphs. Given their observed magnetic behaviors, we propose α−KTi(C₂O₄)₂⋅xH₂O and β−KTi(C₂O₄)₂⋅2H₂O as close to ideal model S =1/2 Heisenberg square and diamond lattice antiferromagnets, respectively.