GibbsDDRM: A Partially Collapsed Gibbs Sampler for Solving Blind Inverse Problems with Denoising Diffusion Restoration
(2301.12686)Abstract
Pre-trained diffusion models have been successfully used as priors in a variety of linear inverse problems, where the goal is to reconstruct a signal from noisy linear measurements. However, existing approaches require knowledge of the linear operator. In this paper, we propose GibbsDDRM, an extension of Denoising Diffusion Restoration Models (DDRM) to a blind setting in which the linear measurement operator is unknown. GibbsDDRM constructs a joint distribution of the data, measurements, and linear operator by using a pre-trained diffusion model for the data prior, and it solves the problem by posterior sampling with an efficient variant of a Gibbs sampler. The proposed method is problem-agnostic, meaning that a pre-trained diffusion model can be applied to various inverse problems without fine-tuning. In experiments, it achieved high performance on both blind image deblurring and vocal dereverberation tasks, despite the use of simple generic priors for the underlying linear operators.
Overview
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Introduces GibbsDDRM, a novel method for addressing blind inverse problems using Denoising Diffusion Restoration Models (DDRM) and a partially collapsed Gibbs sampler.
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This approach does not require detailed knowledge of the corrupting linear operator and leverages pre-trained diffusion models, offering versatility across various applications.
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Experimental results in blind image deblurring and vocal dereverberation show GibbsDDRM's superior performance over existing methods.
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The method's ability to generalize across different problems without specific tuning is seen as a significant advancement for adaptable and efficient AI systems.
GibbsDDRM: A Novel Approach for Solving Blind Inverse Problems using Diffusion Models
Introduction to Blind Inverse Problems
Blind inverse problems represent a significant challenge within various domains, notably in the fields of image and audio processing. These problems entail reconstructing original signals or images from observed data that have been distorted by an unknown linear operator. Traditional methods for tackling such challenges often rely on specific assumptions or extensive training data for distinct problems, limiting their versatility and application scope.
The Proposed Solution: GibbsDDRM
In a novel extension of Denoising Diffusion Restoration Models (DDRM), a study introduces GibbsDDRM to address these challenges without presupposing detailed knowledge of the corrupting linear operator. This innovative method combines the strengths of pre-trained diffusion models with a partially collapsed Gibbs sampler (PCGS) to achieve remarkable results in blind settings.
GibbsDDRM constructs a joint distribution that encapsulates the data, the measurements, and the parameters of the linear operator. An efficient sampling method derived from PCGS allows the model to approximate samples from the posterior distribution of the data and the linear operator’s parameters, given the observed measurements. Notably, this approach leverages simple, generic priors for the measurement process parameters, circumventing the need for intricate prior models.
Theoretical Foundations and Experimental Validation
Providing a rigorous theoretical foundation, the model is validated through extensive experimentation, showing its efficacy in challenging scenarios like blind image deblurring and vocal dereverberation. The use of pre-trained diffusion models, key to this approach, enables the application of GibbsDDRM across diverse inverse problems without the necessity for retraining. Experimental results, particularly in blind image deblurring tasks, illustrate GibbsDDRM's superior performance, achieving high scores in terms of perceptual similarity and faithfulness to the original images. Similarly, in vocal dereverberation, GibbsDDRM outshines existing methods, offering a new benchmark in processing quality and signal restoration.
The Methodology in Detail
The methodology hinges on efficiently sampling from complex posterior distributions, leveraging pre-trained diffusion models' capabilities to model data distributions. By introducing a partially collapsed Gibbs sampler, GibbsDDRM enhances sampling efficiency, consequently improving the estimation accuracy of both the original signal and the latent parameters of the linear operator.
Implications and Future Prospects
The implications of GibbsDDRM are vast for the future of AI and machine learning, especially in solving inverse problems. This method's ability to generalize across different problems without specific tuning suggests a significant step forward in creating more adaptable and efficient AI systems.
The exploration into blind inverse problem-solving paves the way for future research, especially regarding the customization of diffusion models and sampling techniques for even broader application spectra. Furthermore, the results encourage a deeper investigation into the theoretical aspects of diffusion-based methods and their potential in addressing a wide array of inverse problems in science and engineering.
Closing Thoughts
GibbsDDRM represents a significant advancement in the realm of AI, particularly in solving blind inverse problems through generative models. Its innovative use of diffusion models in combination with a tailored Gibbs sampler highlights the growing importance of adaptable and theory-driven approaches in the evolution of machine learning technologies. As research continues, GibbsDDRM's contributions will undoubtedly influence future developments in AI, pushing the boundaries of what is possible in solving complex inverse problems across various domains.
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GitHub - sony/gibbsddrm (22 stars)