I have a latent variable model that represents p(x) using two Gaussian distributions p(z) and p(x|z). The mean and covariance of p(x|z) is represented by some function of z using a neural network.

Problem:
I want to find the level curve (contour) of p(x) corresponding to p(x) = 1.
What are (efficient) ways of doing this?

My thought process thus far:

1. Use contour finding functions of inbuilt packages in matlab (etc) in some way.
2. Do some form of sampling from p(x) to obtain the level curve. Possible direction: sample from the distribution 1 / (1 – p(x)) this will generate samples with high probability near the required contour, then use some method to approximate the curve itself from the sampled points.