  We introduce discriminator guidance in the setting of Autoregressive
Diffusion Models. The use of a discriminator to guide a diffusion process has
previously been used for continuous diffusion models, and in this work we
derive ways of using a discriminator together with a pretrained generative
model in the discrete case. First, we show that using an optimal discriminator
will correct the pretrained model and enable exact sampling from the underlying
data distribution. Second, to account for the realistic scenario of using a
sub-optimal discriminator, we derive a sequential Monte Carlo algorithm which
iteratively takes the predictions from the discrimiator into account during the
generation process. We test these approaches on the task of generating
molecular graphs and show how the discriminator improves the generative
performance over using only the pretrained model.
