The setting is an ergodic dynamical system ( X , μ ) whose points are themselves uniformly discrete point sets Λ in some space R d and whose group action is that of translation of these point sets by the vectors of R d . Steven Dworkin’s argument relates the diffraction of the typical point sets comprising X to the dynamical spectrum of X . In this paper we look more deeply at this relationship, particularly in the context of point processes. We show that there is an R d -equivariant, isometric embedding, depending on the scattering strengths (weights) that are assigned to the points of Λ ∈ X , that takes the L 2 -space of R d under the diffraction measure into L 2 ( X , μ ) . We examine the image of this embedding and give a number of examples that show how it fails to be surjective. We show that full information on the measure μ is available from the weights and set of all the correlations (that is, the two-point, three-point, …, correlations) of the typical point set Λ ∈ X . We develop a formalism in the setting of random point measures that includes multi-colour point sets, and arbitrary real-valued weightings for the scattering from the different colour types of points, in the context of Palm measures and weighted versions of them. As an application we give a simple proof of a square-mean version of the Bombieri–Taylor conjecture, and from that we obtain an inequality that gives a quantitative relationship between the autocorrelation, the diffraction, and the ϵ -dual characters of typical element of X . The paper ends with a discussion of the Palm measure in the context of defining pattern frequencies.