Rebuttal (Part 3)
> **Q:** *Whether more conditional slides will make numerical performance better?*
A: We perform experiments that train our conditional model (DiffusionBlend) on 0, 2, 4, 6 conditional slices and evaluate on the LIDC dataset with 8 projections. Results show that including conditional slices increases the performance significantly, but adding more conditional slices is not guaranteed to further improve the performance and the improvement may be marginal.
To explain why the improvement is marginal with more conditioning slices, we can think about the iterative process of diffusion reverse sampling [1,2]. For example, if using 2 conditional slices, for one specific slice, the first iteration conditions on 2 neighboring slices, but its neighbors also conditions on 2 additional slices. At the second iteration, that slice still conditions on its neighbors (which already had information from 2 additional slices), so it can get the information from the condition of 4 slices, by tracing back to the first iteration. In this way, we can show that with sufficient number of iterations, one specific slice can take the information (condition) on every other slice. Since we have sufficient number of iterations, either 2,4 or 6 conditional slices enables us to condition one slice on all other slices eventually.
This method enables us to learn the 3D prior very ***efficiently*** with minimal number of conditioning slices.
| Conditioning slices | PSNR/SSIM (8 views)|
|------| ------|
|0 | 30.98/0.894|
|2 | 33.73/0.933|
|4 | 33.32/0.932 |
|6 | 33.53/0.936 |
> **Q:** *The adjacent slices of different 3D patches still cannot be updated simultaneously*
A: Previous work [1,3] demonstrate that each step of summation, gradient descent, or even ADMM updates can be split into each step of diffusion reverse sampling process while achieving satisfying performance. Here even though the adjacency slices may not be updated simultaneously at consecutive reverse sampling iterations, it is similar to a Monte Carlo average of the score of the distribution of different partitions as demonstrated in Eq.7. So the goal is not to compute the score of the 3D patch distribution as in Eq.5, but to approximate the score of the ground truth distribution p(x) by averaging the scores of the distributions of multiple partitions.
[1] Chung, Hyungjin, et al. "Solving 3d inverse problems using pre-trained 2d diffusion models." Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2023
[2] Chung, Hyungjin, Suhyeon Lee, and Jong Chul Ye. "Decomposed Diffusion Sampler for Accelerating Large-Scale Inverse Problems." The Twelfth International Conference on Learning Representations.
[3] Lee, Suhyeon, et al. "Improving 3D imaging with pre-trained perpendicular 2D diffusion models." Proceedings of the IEEE/CVF International Conference on Computer Vision. 2023.
[4] Song, Yang, et al. "Solving Inverse Problems in Medical Imaging with Score-Based Generative Models." International Conference on Learning Representations.
[5] Chung, Hyungjin, et al. "Improving diffusion models for inverse problems using manifold constraints." Advances in Neural Information Processing Systems 35 (2022): 25683-25696.
[6] Ye, Siqi, et al. "SPULTRA: Low-dose CT image reconstruction with joint statistical and learned image models." IEEE transactions on medical imaging 39.3 (2019): 729-741.
[7] Goldstein, Tom, and Stanley Osher. "The split Bregman method for L1-regularized problems." SIAM journal on imaging sciences 2.2 (2009): 323-343.