Paper: Unpaired Image-to-Image Translation via Neural Schrödinger Bridge (ICLR-2024)

Reviewer comment (Experiments):
It could be valuable to include the reverse translations (such as Zebra to Horse, Winter to Summer) in the supplementary material, providing more comprehensive experimental results.

Author response:
We thank the Reviewer for the insightful review, which has been incorporated into the revised paper. We address the Reviewer's concern below.

> **Q1 : It could be valuable to include the reverse translations (such as Zebra to Horse, Winter to Summer) in the supplementary material, providing more comprehensive experimental results.**

We kindly refer the Reviewer to Appendix C.5, where we provided an additional result on Zebra2Horse translation, and observed UNSB beats CycleGAN. We plan to include more results in the future.

Reviewer comment (Experiments):
I think that some relevant baselines were not included in the experimental section. Could the author compare the proposed method to EGSDE [1] (Diffusion-based model)?  

[1] Zhao et al. EGSDE: Unpaired Image-to-Image Translation via Energy-Guided Stochastic Differential Equations. In NeurIPS, 2022.

Author response:
We kindly refer the Reviewer to Appendix C.3, where we compared UNSB with EGSDE, StarGAN v2, and NOT on the Male2Female translation task, and observed UNSB beats all baselines.

Reviewer comment (Experiments):
Following my previous point, the datasets considered in the paper are all of “scene-level" image to image translation (in which mostly color and texture need to be altered during translation). In most of other I2I translation works, many "object-level" datasets are evaluated e.g. CelebA-HQ Male-to-Female, Cat-to-dog, etc. Do the authors expect different performance for the latter case? I believe it would be helpful to include benchmarks for at least some of these additional datasets to understand the strengths and the limitations of the proposed method.

Author response:
We kindly refer the Reviewer to Appendix C.3, where we performed an additional experiment on Male2Female, and observed good results for UNSB.

Reviewer comment (Experiments):
The description of the Stochasticity analysis (Fig. 7) is not clear to me. Could the author describe this ablation experiment and what does the generated map tell us? I understand that high pixel-wise std implies greater diversity, but why is it surprising that the std is greater for the foreground pixels? What is the scale of the std?

Author response:
The following discussion has been added to Appendix C.2.

Fig. 7 serves as evidence that UNSB indeed solves the SB problem. Specifically, a SB between two domains is stochastic, so it does one-to-many translation. Thus, a necessary condition for a model to be a SB is stochasticity. Fig. 7 shows that UNSB satisfies this necessary condition. 

Greater std for foreground pixels tells us UNSB does one-to-many generation, and generated images lie in the target domain. For instance, a model which simply adds Gaussian noise also does one-to-many generation, but is not meaningful. UNSB output shows high variation for locations which are relevant to the target domain (Zebra).

Minimum and maximum values of pixel standard deviation in Figure 7 are 0.0031 and 0.7940, respectively. We note that all pixel values are normalized into [0,1].

Reviewer comment (Experiments):
Regarding the competitive methods (GANs), the authors miss the StarGAN and StarGAN v2 [3]. The latter model demonstrates a good quality on the unpaired image2image and I think this model is a good baseline method. Please, add it to the comparison.

Author response:
We kindly refer the Reviewer to Appendix C.3, where we compared UNSB with StarGAN v2, EGSDE, and NOT on the Male2Female translation task, and observed UNSB beats all baselines.

Reviewer comment (Theory):
I have one concern about objective (14). The transition from constrained problem (9)-(10) to the combination of losses (14) is non-trivial and not fully theoretically justified. I am not sure that the objective (14) indeed solves the SB problem. Some comments/clarifications will contribute to the clearness of the manuscript flow.

Author response:
Thanks for the important comment. The transition from constrained problem to an unconstrained formulation arises from using the Langragian and dual formulation. Furthermore, we would like to refer the Reviewer to Appendix C.4, where we added a result on the suggested benchmark [4], and observed positive results.

Reviewer comment (Writing):
I ask the authors to add the clarifications how to estimate the entropy with samples, a technique introduced at the beginning of page 6. It will facilitate the comprehension and smoothness of the reading.

Author response:
Thank you for the constructive feedback. We provided more detail on entropy calculation in Appendix B of the revised paper.

Reviewer comment (Experiments):
I strongly encourage the authors to evaluate how their approach solves the SB problem on a nontrivial setup beyond the gaussian2gaussian case. In particular, there is a recent paper [4] which proposes benchmark pairs of distributions with known GT EOT/SB solutions, even for image data. The validation on such a benchmark will highly contribute to the quality of the paper and will probably answer the question (3).

Author response:
Thanks for the important comment. The transition from constrained problem to an unconstrained formulation arises from using the Langragian and dual formulation. Furthermore, we would like to refer the Reviewer to Appendix C.4, where we added a result on the suggested benchmark [4], and observed positive results.