* The visual quality/fidelity of the generated images is quite low. Making sure that the visual fidelity on common metrics such as FID matches or is at least close enough to GAN models will be useful to validate that the approach supports high fidelity (as otherwise it may be the case that it achieves compositionality at the expense of lower potential for fine details or high fidelity, as is the case in e.g. VAEs). Given that there have been many works that explore combinations of properties for CelebA images with GANs, showing that the proposed approach can compete with them is especially important. * It is unclear to me if MCMC is efficient in terms of training and convergence. Showing learning plots as well compared to other types of generative models will be useful. * The use of energy models for image generation is much more unexplored compared to GANs and VAEs and so exploring it further is great. However, note that the motivation and goals of the model -- to achieve compositional generation through logical combination of concepts learned through data subsets, is similar to a prior VAE paper. See further details in the related work review part. * Given the visual samples in the paper, it looks as if it might be the case that the model has limited variability in generated images: the face images in figure 3 show that both in the second and 4th rows the model tends to generate images that feature unspecified but correlated properties, such as the blonde hair or the very similar bottom three faces. That’s also the case in figure 5 rows 2-4. Consequently, it gives the sense that the model or sampling may not allow for large variation in the generated images, but rather tend to take typical likely examples, as happened in the earlier GAN models. A quantitative comparison of the variance in the images compared to other types of generative models will be useful to either refute or validate this.
* The use of energy models for image generation is much more unexplored compared to GANs and VAEs and so exploring it further is great. However, note that the motivation and goals of the model -- to achieve compositional generation through logical combination of concepts learned through data subsets, is similar to a prior VAE paper. See further details in the related work review part.