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A book I was reading stated that diffusion can exist without a gradient of a physical quantity. Heat is an example of diffusion because of temperature gradient and similar is the case of mass flow in chemistry. Can anyone give me an example for a gradient less diffusion process?

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I would guess you mean self diffusion: see http://en.wikipedia.org/wiki/Self-diffusion for details.

Suppose you take an aqueous solution of (for example) salt that is uniform so there are no concentration gradients. There is no net diffusion, but the sodium and chloride ions wander around due to random thermal motion, so if you watch a particular sodium atom it will "diffuse" around in a random walk motion.

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Although I still feel that random motions occur because of gradients (temporal if necessary) this is a good example! – Fluidman May 17 '12 at 16:39
@Fluidman What about Brownian motion? Gradients and diffusion constants are only macroscopically defined. – Bernhard May 17 '12 at 18:39

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