How can we sample from GFN unconditionally in discrete vae case?

[bugrabaran]

In paper it says "VQ-VAEs assume a uniform prior over the discrete latents 𝑧. However, GFlowNet-EM enables us to also learn a prior distribution, 𝑝 𝜃 (𝑧), jointly with the decoder 𝑝 𝜃 (𝑥|𝑧)." in section 5.3. If I am not mistaken we should be able to generate unseen examples/data by sampling from the encoder/gfn and give this as an input to the decoder. But I am confused about how we can sample from this learned prior? Is it going to come from PixelCNN which is trained with gfn in parallel?

Any help is much appreciated!

[AlexGraikos]

In the setting where we use a PixelCNN to learn the prior (instead of assuming it is uniform) you can directly sample a latent representation from the trained PixelCNN and decode it into an image. Section D in the Appendix describes it in more detail.

In the code, you can look at the sample_prior(prior, batch_size) function in train_gfn_prior.py (line 15) where for each of the latents in the $l_h \times l_w$ latent grid we sample a categorical value.

[bugrabaran]

Thanks for the explanation !