This time I paid attention. They went right past the images of floaters in my eye. So they are on a different plane. They moved at what seemed like nearly uniform speeds, although they sometimes went in arced trajectories. Each disappeared individually, sometimes seeming to radiate from a point, acting a bit like sparks in fireworks. They all remained in focus.
Combined with uniform speed, this suggests they are all in the same plane. Two planes suggest themselves: my retina or the outer surface of my eye. If the retina, it might be some sort of nonlinear interaction between photoreceptors, producing "gliders" similar to those in the Game of Life.
If the surface of the eye, they might be lipid droplets moving under gravity as my tear film drains and evaporates between blinks. I've seen these before, so I either have a chronic eye infection or they are not alive*, despite their swimming behavior. I do not have "dry eye".
This may be a common phenomenon. I described it to a friend, who confirmed he has seen the same. But I have not been able to find a description of this strange visual phenomenon in the literature on thin film drainage, the Marangoni effect, floaters, or dry eye and tear film behavior. Floaters drift slowly, despite their Latin name Muscae volitantes ("flying flies").
If you know how to visualize it so others could see what I see, or reproduce it experimentally, or can show that it's a rediscovery, please let me know. In any case, try observing this phenomenon with your own eyes. If you're good at drawing, send me a sketch of what you see.
*Hanczyc, M.M., Toyota, T., Ikegami, T., Packard, N. and Sugawara, T. (2007) Fatty acid chemistry at the oil-water interface: Self-propelled oil droplets. Journal of the American Chemical Society 129, 9386-9391.