Impatiens must form seeds to naturalize in your garden, so do not deadhead spent blossoms. When you allow plants to bloom to their heart's content and keep them well watered, many impatiens species will form seeds. When the seeds are ready, they will naturally drop to the ground, and when conditions are suitable, they will sprout and grow into additional plants.
Snails and slugs can decimate young impatiens plants. If these creatures are common nighttime marauders in your garden, scatter diatomaceous earth or iron phosphate granules on the soil surface surrounding your adult plants. When seedlings appear, the slugs and snails will not be able to reach them because of the organic controls you put in place to deter or kill them.
Baby impatiens plants will not be able to sprout and grow if the area where their seeds landed is thick with weeds. Sometimes grass will spread into flowerbeds, so if your existing Impatiens grow in a border bed near a lawn, take care to pull it out in the flowerbed where you want your impatiens to spread and grow. Pull all other weeds as well.
If your existing Impatiens plants do not seem to be producing seeds and spreading by themselves, start more plants by taking cuttings and rooting them. Snip off 3- to 4-inch nonblooming tips of an existing impatiens plant, if they're available. Strip off lower leaves and dip each one into a commercial rooting hormone. Plant in small pots filled with damp potting soil; keep in a shady spot and keep well watered.