Diffuse means to spread out. Candlelight can diffuse a soft glow throughout a room. A diffuse idea is one that spreads from person to person, and a diffuse speech is scattered and unclear.
As a verb, diffuse means to spread something out, but also applies to spreading things such as ideas or culture so that they become widely known. When something is diffused, it's mixed in, and when you drop propaganda pamphlets out of airplanes you're diffusing the propaganda. The adjective comes from Latin diffusus, from diffundere "to pour in different directions," from the prefix dis- "apart" plus fundere, "to pour."