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Small diffusers do little to enlarge the size of the light source, and so do not, in themselves, soften the light very much. What they actually do is redistribute the flash unit's light output so there's more light scattering around, bouncing off walls and ceilings and so on. They help to reduce the "black hole" effect of flash photography by distributing light more evenly and thus providing illumination to the background scene. They also soften the light a little for foreground subjects.
Small diffusers are best suited for small interior spaces or for macro photography shot without a macro unit. They are less useful when shooting outdoors or in dark interior spaces, where there's no way to bounce the light. In such situations they simply cut down usable range, waste power (plus batteries and money) and increase flash cycle time. They're also problematic when the walls or ceilings are painted bright colors, as the light bouncing off those surfaces will have a color cast. Small diffusers also offer less control, as they just basically spray light around. But all this aside, they can be very useful, particularly for fast-moving journalist or wedding situations.