My plant is afflicted with weeds

My plant is afflicted with weeds

Hello, all! I have several different house plants (no yard in which to garden, I'm afraid - so potted plants will do for now!) and something recently came to my attention: My coleus plant, which I've had for ~2.5 years, recently began to sprout little green leaves all throughout the soil. I don't recall having seen these before so I'm wondering if my plant is somehow now being afflicted with weeds? If so, what's the easiest way to rid the poor thing of these jerks? Is it possible that they are just tiny little baby coleus starting out on their own, independent of the main stalk? Thanks!
Freebies!

Freebies!

these were taken about a week ago… things have changed since i will post asap

these were taken about a week ago… things have changed since i will post asap

Christmas Frou-Frou

Christmas Frou-Frou

mexican sour gherkin

mexican sour gherkin

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Pics and questions

i totally heart my room!

i totally heart my room!