In VAE, why are we approximating p(z|x) using q(z) and not q(z|x) I am watching this lecture on VAE:
https://www.youtube.com/watch?v=uaaqyVS9-rM&t=1507s
and at 26:00, it is stated that the goal is the minimize the KL div. between the distribution we are trying to find - p(z|x) by approximating it with another distribution: q(z). but why aren't we using q(z|x)?

The evidence lower bound we're trying to maximize is valid for any choice of $q(z)$, so for example, you could just arbitrarily choose $q(z) = \mathcal{N}(0,1)$, but this wouldn't yield a very good bound.
Since we can use any $q(z)$ for any given $x$, we might as well have our $q(z)$ depend on $x$, and this is written as $q(z|x)$ -- admittedly maybe some notation like $q(z) = r(z;x)$ would be less confusing.
TLDR: $q(z|x)$ is just a special case of all the possible $q(z)$'s that we could choose from.
