Response to Reviewer 5bsx
Thank you for taking your time reviewing our paper. We are glad that the reviewer thinks that “the proposed method is sound” and that the “experimental results well verified the effectiveness of the proposed method”. Please find below our response to your concerns.
- Re Weakness 1: As the reviewer points out, DiracDiffusion is a solver for inverse problems with *known* forward model. This is a clear distinction from general image restoration techniques that rely only on clean-noisy paired data for training without knowing the corruption process. However, in this general scenario there is no notion of *data consistency*: given a corrupted input and the reconstructed image we are unable to evaluate how well the reconstruction explains the input (without a ground truth). In stark contrast, our work focuses on inverse problems with known forward models, a common case in real-world problems where the physical process producing the observations is known (known camera blur, microscopy with known probe function, medical imaging problems such as CT or MRI etc). In this setting, a crucial requirement is data consistency: the reconstruction has to be consistent with the noisy measurement as dictated by the forward model. In fact, ensuring this consistency while producing exceptional image fidelity is the main goal of our paper. We would like to also highlight that other diffusion-based solvers overwhelmingly assume a known forward model as well ([1-3]). To address the reviewer’s concern we updated the main text to better emphasize this assumption.
- Re Weakness 2: Our early stopping method is indeed straightforward and intuitive, yet very effective. Furthermore, the early stopping technique is an interesting consequence of our proposed Stochastic Diffusion Process framework, and not the sole contribution of our work.
- Re Weakness 3: Thank you for pointing this out, we added the specific form of the degradation process in Appendix F. We emphasize that $\mathcal{A}_t(\cdot)$ is designed a priori based on the known forward model and its time-dependence (scheduling) is determined via the degradation scheduling algorithm in Algorithm 2 in the appendix.
- Re Weakness 4: We point out that when the degradation process is linear ($\mathcal{A}_t(\cdot)$ is a linear mapping), reconstructing $\mathcal{A}_t(x_0)$ is not equivalent to reconstructing $x_0$ as the linear mapping is typically not invertible (as is the case in deblurring or inpainting). In fact, as we highlight in the paper, predicting $\mathcal{A}_t(x_0)$ from the noisy and degraded input (denoising only) is an easier problem than completely reconstructing $x_0$ in one step (denoising and reconstruction/inversion).
Thank you for catching the typo, we fixed it in the new version. We are happy to discuss further if there are additional concerns and would like to ask the reviewer to consider raising their score in case we addressed all major issues.
[1] Kawar, Bahjat, et al. "Denoising diffusion restoration models." Advances in Neural Information Processing Systems 35 (2022): 23593-23606.
[2] Chung, Hyungjin, et al. "Diffusion posterior sampling for general noisy inverse problems." arXiv preprint arXiv:2209.14687 (2022).
[3] Song, Yang, et al. "Solving inverse problems in medical imaging with score-based generative models." arXiv preprint arXiv:2111.08005 (2021).