Spread, circulate, disseminate, diffuse, propagate, radiate can all mean to extend or cause to extend over an area or space.
Spread basically implies a drawing or stretching out to the limit and in the sense here considered emphasizes distribution or dispersion (as by strewing or scattering or being strewed or scattered) over an extent of space that may be large or small or incalculable or calculable.
Often it suggests an applying in or a taking the form of a thin layer or a making or becoming more prevalent or more widely known or felt.
Circulate may imply in its primary and largely technical use a continuous or repeated movement over the same course from starting point to starting point.
In its more general applications the term tends to stress a moving about or a causing to move about freely and continuously, often to the more or less complete loss of the notion of going over the same course again and again.
Disseminate implies much the same as spread when that word suggests distribution here and there.
Diffuse suggests a spreading throughout a space; it is applied primarily to things (as sound, light, odor, or vapor) that in moving permeate the medium through which they move and in its extended sense to things (as education, knowledge, fame, and spirit) that have or are felt to have a similar pervasive quality in their dissemination.
Radiate implies a spreading from a center outward in or as if in rays; in general use it is often applied to the spreading of something material or immaterial from a fixed center, but in its common technical use the term is largely restricted in reference to diffusion in the form of rays (as of heat or light).