Wild Thyme Invasive?

Thank you! You not only answered my questions, but also taught me more about herb cultivation. Would you please help me on another question about thyme?
I heard some stories that growing wild thymes in the garden can be troublesome sometime because they can self sow into lawn and grow like weeds. Is it true that wild thyme can be invasive by self sowing? If it does, how to control it? Do other thyme varieties have the same habit, for example, English thyme, Lemon thyme, Creeping thyme?
Thanks again for your quick response!

Wild thyme (Thymus pulegiodes, syn. T. serpyllum) can be invasive in some situations. It likes full sun exposure and sandy, relatively dry soil. In some areas of eastern Ontario it has escaped from cultivation and established itself along roadsides and in fields. However, as invasives go it is considered a low risk because it is easy to control. Certainly, in a managed garden situation there is little risk of it getting out of hand because simple weeding techniques control it easily. Any seedlings the plants produced are easy to destroy and, in our experience, the seeds do not persist in the soil for years like weeds do.
Creeping thyme (T. praecox and varieties) presents zero threat of becoming weedy because it does not produce seeds and because it spread much more slowly. English thyme is no threat also, even though it produces seeds, because it does not creep like wild thyme and, again, any seedlings it produces are easy to control. None of the many varieties of lemon thyme are particularly invasive, even creeping lemon thyme is little risk because it does not produce seeds and spreads only by creeping.