P3
任务描述
- 图像去噪
- 图像超分
- 图像补全
输入：
输出：
基于某个预训练的diffusion model，在无condition的情况下，每张图像都符合diffusion生成模型的分布。当以某个特定的图像（模糊图像、低分辨率图像）时，期望能够得到的是对应的清晰、高分辨率的图像的分布。
P6
Replacement-based Methods
(Overwrites model prediction with known information)
| ID | Year | Name | Note | Tags | Link |
|---|---|---|---|---|---|
| 2021 | ILVR: Conditioning Method for Denoising Diffusion Probabilistic Models | ||||
| Kawar et al., "SNIPS: Solving Noisy Inverse Problems Stochastically", NeurIPS 2021 | |||||
| Chung et al., "Come-Closer-Diffuse-Faster: Accelerating Conditional Diffusion Models for Inverse Problems through Stochastic Contraction", CVPR 2022 | |||||
| Song et al., "Solving Inverse Problems in Medical Imaging with Score-Based Generative Models", ICLR 2022 | |||||
| Kawar et al., "Denoising Diffusion Restoration Models", NeurIPS 2022 |
P7
Reconstruction-based Methods
(Approximate classifier-free guidance without additional training)
Chung et al., "Diffusion Posterior Sampling for General Noisy Inverse Problems", ICLR 2023
✅ cfg 使用\((x,t)\)的 pair data 来近似 \(\nabla _{x_t} \log p_t(\mathbf{y}|\mathbf{x}_t)\)，但此处没有 pair data，希望通过非训练的方法来得出。
✅ 公式基于马尔可夫推导。\(p(\mathbf{y}|\mathbf{x}_t)\) 可描述为 \(p(\mathbf{y}|\mathbf{x}_0)\) 的期望。然后把期望从外面移到里面。
P8
In the Gaussian case,
$$ p(\mathbf{y} |\mathbb{E} [\mathbf{x} _ 0|\mathbf{x} _ t])=-c||\mathcal{A} \mathbf{(\hat{x}} _ 0)-\mathbf{y} ||^2_2 $$
Maximizing the likelihood is minimizing the L2 distance between measured and generated!
Chung et al., "Diffusion Posterior Sampling for General Noisy Inverse Problems", ICLR 2023
✅ 在 diffusion 的同时做重建。
More
- Video Diffusion/Pyramid DDPM: used for uper-resolution.
- Pseudoinverse guidance: linear and some non-differentiable problems, e.g., JPEG
- MCG: combines replacement & reconstruction for linear problems.
Others
- CSGM: Posterior sampling with Langevin Dynamics based on the diffusion score model.
- RED-Diff: A Regularizing-by-Denoising (RED), variational inference approach.
- Posterior sampling: use RealNVP to approximate posterior samples from diffusion models.
| ID | Year | Name | Note | Tags | Link |
|---|---|---|---|---|---|
| Chung et al., "Improving Diffusion Models for Inverse Problems using Manifold Constraints", NeurIPS 2022 | |||||
| Ryu and Ye, "Pyramidal Denoising Diffusion Probabilistic Models", arXiv 2022 | |||||
| Chung et al., "Diffusion Posterior Sampling for General Noisy Inverse Problems", arXiv 2022 | |||||
| Song et al., "Pseudoinverse-Guided Diffusion Models for Inverse Problems", ICLR 2023 | |||||
| Jalal et al., "Robust Compressed Sensing MRI with Deep Generative Priors", NeurIPS 2021 | |||||
| Mardani et al., "A Variational Perspective on Solving Inverse Problems with Diffusion Models", arXiv 2023 | |||||
| Feng et al., "Score-Based Diffusion Models as Principled Priors for Inverse Imaging", arXiv 2023 |
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https://caterpillarstudygroup.github.io/ImportantArticles/