Thank you for the comment! We appreciate the opportunity to continue the discussion.
> The author has partially addressed my concerns.
Can you please tell us which concerns have not been addressed so we can attend to them as well?
> However, I still think that the presentation of the paper is lacking at this stage.
In our original reply, we kindly asked for specific examples where the language was not up to the NeurIPS level, as it is important to us to have this constructive feedback. Could we please extend the original request here and ask for specifics on where the paper is lacking as well? We have revised the entire paper and followed all suggestions from all reviewers. It would greatly benefit our work to know which parts are lacking, as we understand that this is the main (remaining) issue with the review. Examples of language before the revision (referring to W1) and the presentation after all the implemented changes would help our work, as we believe in the NeurIPS review process and the best practices to help promote research.
> However, since I cannot see the revised paper, I cannot judge whether the final presentation meets the requirements of NeurIPS.
As we cannot upload the full paper, I can kindly point you to the Method section, which is in the global response, and the Experiments section, which is a reply to reviewer wkBK. The Related Work and Foundations sections that were changed can be found below. The rest of the paper remains unchanged, so the full paper is now shown in our replies.
>
> # Related Work
> Pre-trained DMs are following a ... each new version [30]. It is clear that there is demand for increasingly higher resolution generation.
> Currently, generating images ... application.
> ## Trained models
> (unchanged)
> ## Adapted models
> (unchanged)
> # Foundations
> ## Diffusion models
> DMs [15,42] are probabilistic generative models that first add noise to a distribution during diffusion and then learn to remove this noise during denoising. During training, a Gaussian probability distribution is learned, and during inference, sampling from the Gaussian leads to the data probability distribution. Executing this process in the latent space [37] is more resource-efficient, allowing for faster training and inference times.
> In formal terms, for a Latent Diffusion Model, if $z_0$ represents the data point in the latent space, given $z_0 \sim q(z_0)$ and $q$ being the diffusion process, then for timesteps t $\in$ $\{1,T\}$ $z_1,\ldots,z_T$ noisy latents, with variance $\beta_t \in (0,1)$, are produced, defining a joint distribution conditioned on $z_0$:
>
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>
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>
> The training estimates an isotropic Gaussian distribution for $z_T$. During the denoising process we sample from $z_T \sim \mathcal{N}(0,{I})$ and remove the added noise using a neural network:
>
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> ## Patch sampling
> The default denoising process of an LDM involves sampling the entire latent space at each timestep. While this approach works for lower resolutions, it becomes increasingly resource-intensive as the resolution increases.
> Instead, we modify the default process to denoise patches of a fixed dimension $128^{2}$ as introduced by DiffInfinite [1]. At each timestep, random patches are selected for denoising, and this process is repeated until the entire latent space is denoised (see Appendix Patch sampling). The DiffInfinite process relies on segmentation masks to condition each individual patch, providing rich spatial information. In a text-to-image DM, where the text-prompt is global for the entire latent space, using this method means that each patch is denoised with the same condition—the text-prompt. This leads to multiple repetitions of the condition and results in poor-quality generations. To address this, we implement a series of key components that enable scaling a pre-trained DM to resolutions never achieved before.
The above changes result in considerably smaller pre-Method sections, allowing the new, better-explained Method section to fit and enhance readability. The previous full text of this section will become a new appendix, titled "Patch sampling," with the addition of our explanation to question 2 of Rv T7y4. Nothing else changes or is added, so this appendix will not be new to you.