Simulated annealing (basically MCMC sampling with a temperature schedule) is how you optimise or sample the equivalent MRF, which I discussed in my other comment. You can hope to escape local minima using annealing, and lower the temperature to zero to fall into a local minima, minimising the noise added by annealing. In practice if you're trying to produce something that looks like a target image as in the article I'm pretty sure the results will be indistinguishable. If you actually cared about how many individual pixels are correct, yes, annealing is better than gradient descent. That's why stochastic gradient descent is used in ML.