Diffusiophoresis is the spontaneous motion of colloidal particles or molecules in a fluid, induced by a concentration gradient of a different substance. In other words, it is motion of one species, A, in response to a concentration gradient in another species, B. Typically, A is colloidal particles which are in aqueous solution in which B is a dissolved salt such as sodium chloride, and so the particles of A are much larger than the ions of B. But both A and B could be polymer molecules, and B could be a small molecule. For example, concentration gradients in ethanol solutions in water move 1 μm diameter colloidal particles with diffusiophoretic velocities  of order 0.1 to 1 μm/s, the movement is towards regions of the solution with lower ethanol concentration (and so higher water concentration). Both species A and B will typically be diffusing but diffusiophoresis is distinct from simple diffusion: in simple diffusion a species A moves down a gradient in its own concentration.
Diffusioosmosis, also referred to as capillary osmosis, is flow of a solution relative to a fixed wall or pore surface, where the flow is driven by a concentration gradient in the solution. This is distinct from flow relative to a surface driven by a gradient in the hydrostatic pressure in the fluid. In diffusioosmosis the hydrostatic pressure is uniform and the flow is due to a concentration gradient.
Diffusioosmosis and diffusiophoresis are essentially the same phenomenon. They are both relative motion of a surface and a solution, driven by a concentration gradient in the solution. This motion is called diffusiophoresis when the solution is considered static with particles moving in it due to relative motion of the fluid at the surface of these particles. The term diffusioosmosis is used when the surface is viewed as static, and the solution flows.
A well studied example of diffusiophoresis is the motion of colloidal particles in an aqueous solution of an electrolyte solution, where a gradient in the concentration of the electrolyte causes motion of the colloidal particles. Colloidal particles may be hundred of nanometres or larger in diameter, while the interfacial double layer region at the surface of the colloidal particle will be of order the Debye length wide, and this is typically only nanometres. So here, the interfacial width is much smaller than the size of the particle, and then the gradient in the smaller species drives diffusiophoretic motion of the colloidal particles largely through motion in the interfacial double layer.
Diffusiophoresis was first studied by Derjaguin and coworkers in 1947.