Accelerating Diffusion Models for Inverse Problems through Shortcut Sampling

Core Concepts

The core message of this paper is to propose a novel pipeline called Shortcut Sampling for Diffusion (SSD) that can efficiently solve inverse problems in a zero-shot manner by modifying the forward process of diffusion models to obtain a transitional state that bridges the gap between the input measurement image and the target restoration.

Abstract

The paper proposes a novel approach called Shortcut Sampling for Diffusion (SSD) to solve inverse problems in a zero-shot manner using diffusion models. The key idea is to modify the forward process of diffusion models to obtain a specific transitional state that serves as a bridge between the input measurement image and the target restoration, rather than starting from random noise as in previous methods.
The paper first discusses the limitations of existing methods that primarily focus on modifying the posterior sampling process. It then introduces Distortion Adaptive Inversion (DA Inversion), a novel inversion technique that can derive the transitional state by incorporating a controllable random disturbance at each forward step. This allows the transitional state to preserve essential information from the input image while adhering to the predefined noise distribution, enabling efficient and precise restoration.
During the generation process, the paper utilizes the generative priors of diffusion models to produce extra details and texture, and introduces a back projection technique as additional consistency constraints to ensure the restored image aligns with the input image in the degenerate subspace.
The paper further proposes an enhanced version called SSD+ that makes SSD suitable for noisy situations or inaccurate estimation of the degradation operator. Experiments on various inverse problems, including super-resolution, colorization, inpainting, and deblurring, demonstrate the effectiveness of the proposed SSD framework, achieving competitive results with significantly fewer neural function evaluations (NFEs) compared to state-of-the-art zero-shot methods.

Stats

The proposed SSD method achieves PSNR of 28.84, FID of 32.41, and LPIPS of 0.202 on 4x super-resolution task on CelebA dataset, using only 30 NFEs.
On the ImageNet dataset, SSD-100 achieves PSNR of 27.45, FID of 37.69, and LPIPS of 0.248 on 4x super-resolution task, outperforming state-of-the-art methods.
SSD-30 outperforms other fast sampling methods like DDRM-30 and DDNM-30 in perception-oriented metrics (FID, LPIPS) on various inverse problems.

Quotes

"By employing a shortcut path of "Input - E - Target"(H†y →xt →x0) instead of the previous "Noise-Target"(xT →x0), SSD enables precise and fast restoration."
"To address this dilemma, we introduce Distortion Adaptive Inversion (DA Inversion). By incorporating a controllable random disturbance at each forward step, DA Inversion is capable of deriving E that adheres to the predetermined noise distribution while preserving the majority of the input image's information."

Key Insights Distilled From

Accelerating Diffusion Models for Inverse Problems through Shortcut Sampling

by Gongye Liu,H... at arxiv.org 05-03-2024

https://arxiv.org/pdf/2305.16965.pdf

Deeper Inquiries

How can the proposed SSD framework be extended to handle more complex degradation operators beyond the ones considered in this work, such as spatially-varying blur or non-Gaussian noise

The proposed SSD framework can be extended to handle more complex degradation operators by incorporating adaptive strategies tailored to the specific characteristics of the degradation. For spatially-varying blur, the framework can integrate spatially varying kernels or filters in the denoising and back projection steps to account for the varying blur across the image. This adaptation can involve learning the spatially varying blur kernels from the input image itself or incorporating prior knowledge about the blur distribution in the training process.
To address non-Gaussian noise, the framework can be enhanced by incorporating robust statistical models that can handle non-Gaussian noise distributions. Techniques such as robust estimation methods or non-parametric approaches can be integrated into the denoising and generation processes to better handle the non-Gaussian nature of the noise. Additionally, the framework can be extended to include adaptive noise modeling techniques that can dynamically adjust to the characteristics of the noise present in the input images.
By incorporating these adaptive strategies and robust statistical models, the SSD framework can effectively handle more complex degradation operators, such as spatially-varying blur and non-Gaussian noise, in a robust and efficient manner.

What are the potential limitations of the SSD approach, and how can it be further improved to handle a wider range of inverse problems or achieve even faster restoration speeds

While the SSD approach has shown promising results in zero-shot image restoration, there are potential limitations and areas for improvement to consider:

Handling Extreme Degradations: SSD may face challenges when dealing with extreme degradation scenarios, such as highly complex noise patterns or severe blurring. To address this, the framework can benefit from incorporating adaptive mechanisms that can dynamically adjust the restoration process based on the severity of the degradation.

Generalization to Diverse Domains: Extending SSD to handle a wider range of inverse problems beyond image restoration may require domain-specific adaptations. Techniques such as transfer learning or domain adaptation can be explored to generalize the framework to diverse domains like audio or video restoration.

Speed and Efficiency: While SSD has shown competitive restoration results with fewer steps, further optimization of the sampling process can enhance the speed and efficiency of the framework. Techniques like parallel processing, optimized network architectures, or hardware acceleration can be leveraged to achieve faster restoration speeds.

Robustness to Uncertainty: Enhancing the robustness of SSD to uncertainty in the degradation operators or noise models can improve its performance in real-world scenarios. Techniques like uncertainty estimation or robust optimization can be integrated to make the framework more resilient to variations in the input data.

By addressing these limitations and incorporating improvements in adaptive strategies, generalization to diverse domains, speed optimization, and robustness to uncertainty, the SSD approach can be further enhanced to handle a wider range of inverse problems and achieve even faster and more efficient restoration speeds.

Given the success of SSD in zero-shot image restoration, how could the insights and techniques developed in this work be applied to other domains beyond computer vision, such as audio or video restoration

The insights and techniques developed in the SSD framework for zero-shot image restoration can be applied to other domains beyond computer vision, such as audio or video restoration, by adapting the framework to the specific characteristics of these domains. Here are some ways the insights from SSD can be applied:

Audio Restoration: In audio restoration, the principles of denoising and back projection can be applied to remove noise, enhance audio quality, and restore degraded audio signals. By modeling the degradation process and incorporating adaptive strategies similar to SSD, audio restoration algorithms can achieve improved results in denoising, audio enhancement, and speech recognition tasks.

Video Restoration: For video restoration, the concepts of denoising, generation processes, and back projection can be extended to handle video frames. By applying the SSD framework to video sequences, techniques for video denoising, super-resolution, and artifact removal can be developed. Adaptive strategies for handling temporal dependencies and motion estimation can further enhance the restoration quality in video processing tasks.

Signal Processing: Beyond image, audio, and video restoration, the principles of diffusion models, denoising, and generation processes can be applied to various signal processing tasks. Applications in signal denoising, compression artifact removal, and signal enhancement can benefit from the insights and techniques developed in the SSD framework.

By adapting the SSD framework to these domains, leveraging domain-specific characteristics, and incorporating adaptive strategies tailored to the nature of the signals, the insights and techniques from SSD can be effectively applied to a wide range of inverse problems in audio, video, and signal processing domains.