The speaker says continuous density evolution can be formulated as gradient descent in a continuous domain, eliminating the need for sampling.

“Uh uh because the change over time has proportional to like the uh divergence of the vector field of the the current density. And if you actually if you go and you you write this out in uh kind of without invoking densities, but let's say we invoke this in with points, you see that this is just uh kind of doing gradient descent in continuous domain. And of course it's the cheapest thing at all, because now you no longer do any sampling at all.”