Yes, yeast cells can move by themselves, but only some types of yeast do so, and they use a different mechanism than animals or plants. Here's a breakdown:

* Budding Yeast (Saccharomyces cerevisiae): The most common type of yeast used in baking and brewing is non-motile. They don't have flagella or cilia, the structures that allow other organisms to swim.

* Fission Yeast (Schizosaccharomyces pombe): This type of yeast is able to move by extending thin, finger-like projections called "pseudopods". These projections are used to crawl across surfaces.

So, while most yeast we encounter in everyday life aren't mobile, there are some types that can move, but not in the same way as swimming organisms.