Denoising Diffusion Restoration Models (2201.11793v3)

Abstract: Many interesting tasks in image restoration can be cast as linear inverse problems. A recent family of approaches for solving these problems uses stochastic algorithms that sample from the posterior distribution of natural images given the measurements. However, efficient solutions often require problem-specific supervised training to model the posterior, whereas unsupervised methods that are not problem-specific typically rely on inefficient iterative methods. This work addresses these issues by introducing Denoising Diffusion Restoration Models (DDRM), an efficient, unsupervised posterior sampling method. Motivated by variational inference, DDRM takes advantage of a pre-trained denoising diffusion generative model for solving any linear inverse problem. We demonstrate DDRM's versatility on several image datasets for super-resolution, deblurring, inpainting, and colorization under various amounts of measurement noise. DDRM outperforms the current leading unsupervised methods on the diverse ImageNet dataset in reconstruction quality, perceptual quality, and runtime, being 5x faster than the nearest competitor. DDRM also generalizes well for natural images out of the distribution of the observed ImageNet training set.

• The paper demonstrates a novel unsupervised diffusion method that efficiently solves linear inverse image problems by leveraging spectral decomposition.
• It details a methodology that partitions signal components via singular value decomposition to reduce runtime to as few as 20 neural function evaluations.
• Results on ImageNet show that DDRM delivers a 5x speed boost and higher perceptual fidelity compared to existing unsupervised restoration techniques.

Essay on "Denoising Diffusion Restoration Models"

The paper, "Denoising Diffusion Restoration Models" (DDRM), proposes a novel method for efficiently solving linear inverse problems in image restoration via unsupervised posterior sampling. It leverages the recent advancements in denoising diffusion probabilistic models (DDPMs) to address several computational and flexibility issues associated with previous approaches.

Background and Motivation

Linear inverse problems are pervasive in image processing. These include tasks such as super-resolution, deblurring, inpainting, and colorization. Traditionally, solving these problems requires either problem-specific supervised learning models or unsupervised models using iterative and computationally-heavy approaches. The DDRM aims to balance efficiency and versatility, confronting the limitations of existing architectures that are either tailored to specific problem domains or rely extensively on iterative processing.

Methodology

DDRM introduces a novel approach leveraging the properties of diffusion models for unsupervised learning. The methodology exploits the variational inference framework, using a pre-trained denoising diffusion generative model to serve as a universal prior for any linear inverse problem. By conducting sampling within the spectral space of the degradation matrix, DDRM circumvents the need for supervised training specific to each problem type.

The model effectively partitions the space into contributing and non-contributing components according to the singular value decomposition (SVD) of the degradation matrix. By using a Markov chain that combines the spectral components with the inherent noise characteristics, DDRM efficiently reconstructs images with notable reduction in runtime, achieving competitive results in as few as 20 neural function evaluations (NFEs).

Results

DDRM demonstrates superior performance across several key metrics. On ImageNet’s diverse dataset, it outperforms other leading unsupervised restoration methods such as DGP and SNIPS in terms of reconstruction quality and perceptual fidelity. Notably, DDRM achieves a reconstruction quality improvement of around 5 times better in speed. Additionally, it shows robustness in handling noisy measurements, which is a significant advantage over existing iterative methods that tend to degrade in performance with noise addition.

Implications and Future Directions

The implications of DDRM are profound for image restoration. Its design enables effective generalization to natural images beyond the training distribution, highlighting its practicality in real-world scenarios where data may not adhere strictly to learned distributions. This characteristic promotes significant advancements in fields requiring high adaptability such as medical imaging, where degradation models may vary extensively.

Further, DDRM's success points to promising future research directions in non-linear inverse problems and scenarios where degradation operators are unknown. Moreover, exploring self-supervised frameworks that emulate DDRM's efficiency could enrich the repository of unsupervised models, potentially setting new standards in efficiency for image restoration tasks.

In summary, the "Denoising Diffusion Restoration Models" paper contributes a substantial advancement in the unsupervised approach to image restoration, combining theoretical innovation with practical efficiency. It sets the stage for further exploration into the capabilities of diffusion models, not just as generative mechanisms but as pivotal tools in solving inverse problems across various domains.