reviews: 
Comments: A watermarking method is proposed for embedding watermarks in the diffusion generated images post-processing.  The proposed SuperMark embeds the watermark into initial Gaussian noise using existing techniques and then applies pre-trained Super-Resolution (SR) models to denoise the watermarked noise.
Strengths: * The manuscript provides tests with specific "Adaptive Attacks".
* The supplementary material also provide numerous examples of watermarked images.
Weaknesses: However, post-processing watermarking methods in general have been studied for long time since 1993 and the author only mentioned one method (Rahman, 2013) from the older times. They should have specified that such watermarking methods are spacial-based and frequency-based methods.

The claim of the limitation for other methods from the following sentence does not make sense and denotes that the authors do not have an overall understanding of the digital watermarking process.
"We reveal that their limitations are mostly stemmed from the disentanglement between robustness and fidelity due to the the encoder–noise layer–decoder architecture"
Actually, watermarked image quality, robustness, embedded information capacity and watermark security represent all requirements for a watermarking system and by enforcing each of these requirements actually limits the effects of all the others.

There is no support for the following claim, and the authors should provide theoretical or empirical proofs to support this:
"diffusion process holds inherent robustness against different distortions."

Also the authors do not provide enough discussion about their other claim that:
"diffusion process holds inherent robustness against different distortions."

The contributions claimed at the end Section 1 Introduction sound very general and do not actually represent major advancements in the areas in the way they are formulated. 

Watermark embedding and watermark extraction stages from Sections 3.3 and 3.4 seem rather straightforward and do not bring any novelty. Sentences from Section 3.1 like "The Gaussian noise added to the conditioned image corresponds to the watermark information, allowing the watermark to be injected seamlessly" or "From this reconstructed noise, the watermark can be extracted effectively," are very general and meaningless. There is no new insight in the watermarking embedding and detection process.

For JPEG, additive noise and smoothing the results would have been better presented in some plots where various degrees of distortion caused by the attacks are tested.

The section about "Adoption of Tree-Ring’s watermark injection method" which adopts the method employed in Tree-Ring (Wen et al., 2024) is confusing. The method proposed in the Tree-Ring (Wen et al., 2024) is completely different from the one presented in this manuscript being embedded in the Fourier frequency domain, while this manuscript discusses a spatial embedding watermarking. The description from the Supplementary of Appendix A.1.2 Tree-ring is not that clear either, it mentions "low-frequency modes" but the description is very superficial and it is not clear how the frequencies are calculated.
Recommendation: 3
Reviewer confidence: 4
Soundness/correctness: 1
Clarity: 2