Inelastic neutron scattering measurements are used to determine the wave-vector- and frequency-dependent spin correlation function J(q, ω) within a (110) plane of paramagnetic RbMnF3 at 3·5TN. This simple cubic antiferromagnet is known to have a nearest-neighbour Heisenberg exchange Hamiltonian with S = fraction five-twos and J = 0·28 mev, so that a precise comparison of the results with existing theories can be made without unknown parameters. For q vectors between 0.1 and 0·4 Å-1 (qmax = 0·74 Å-1), the scattering is isotropic in q with a frequency dependence close to a Lorentzian with depressed wings. From the variation of the Lorentzian widths with wave vector the diffusion constant capital Lambda, Greek = 8·0 + 1·0 mev Å2 is deduced, in good agreement with the theory of Bennett and Martin. At larger q vectors the scattering is compared with the Gram-Charlier expansion having the correct second and fourth moments as suggested by Collins and Marshall, and with Fourier transformations of the space- and time-dependent spin correlations calculated by Windsor. Good agreement with these infinite-temperature theories is found throughout the zone except at energy transfers less than 4 mev. The discrepancies at small energies, which are greatest near the antiferromagnetic reciprocal lattice point, are ascribed to the effects of short-range order, and show features in quantitative agreement with the finite-temperature calculations of Sears.