Find inputs that give highest variance in output space
Very interesting question! I didn't get if the out put of one input vector is just one image or a set of images but this does not change the solution much.
I propose you directly learn the relation between input and the variance of output images. For simplicity, I assume you target the pixle-wise variance within an output image. Then your training data would become $\{x_i, Var(y_i)\}_{i=1}^N$ instead of $\{x_i, y_i\}_{i=1}^N$!
Then your problem can be solved as:

Classification: You threshold the &quot;high variance&quot; and discritize your output into high variance and low variance classes
Regression: Even better! you directly learn the value of variance and have more flexibility on interpreting the results at the end (e.g. the thresholding mentioned above can be applied afterwards).

I hope I understood your question right, I was clear and it could help!
Good Luck!