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.

In our main paper, we describe our methods based on the "V ariance Exploding" hyperparameters Therefore, we can use "V ariance Preserving" Note that although the inference algorithms are shown to be equivalent, the choice between "V ariance Preserving" and "V ariance Exploding" may affect the training of diffusion networks. The proof uses a basic property of Gaussian marginals (see [ 4 ] for the complete version). In denoising, the corrupted image is the original image with additive white Gaussian noise. Equation 23 is the SVD of H . The grayscale image is obtained by averaging the red, green, and blue channels of each pixel.

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.

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. 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 5\times faster than the nearest competitor.

Diffusion models have emerged as a promising class of generative models that map noisy inputs to realistic images. More recently, they have been employed to generate solutions to partial differential equations (PDEs). However, they still struggle with inverse problems in the Laplacian operator, for instance, the Poisson equation, because the eigenvalues that are large in magnitude amplify the measurement noise. This paper presents a novel approach for the inverse and forward solution of PDEs through the use of denoising diffusion restoration models (DDRM). DDRMs were used in linear inverse problems to restore original clean signals by exploiting the singular value decomposition (SVD) of the linear operator. Equivalently, we present an approach to restore the solution and the parameters in the Poisson equation by exploiting the eigenvalues and the eigenfunctions of the Laplacian operator. Our results show that using denoising diffusion restoration significantly improves the estimation of the solution and parameters. Our research, as a result, pioneers the integration of diffusion models with the principles of underlying physics to solve PDEs.

Recent years have witnessed a rapid development of deep generative models for creating synthetic media, such as images and videos. While the practical applications of these models in everyday tasks are enticing, it is crucial to assess the inherent risks regarding their fairness. In this work, we introduce a comprehensive framework for benchmarking the performance and fairness of conditional generative models. We develop a set of metrics$\unicode{x2013}$inspired by their supervised fairness counterparts$\unicode{x2013}$to evaluate the models on their fairness and diversity. Focusing on the specific application of image upsampling, we create a benchmark covering a wide variety of modern upsampling methods. As part of the benchmark, we introduce UnfairFace, a subset of FairFace that replicates the racial distribution of common large-scale face datasets. Our empirical study highlights the importance of using an unbiased training set and reveals variations in how the algorithms respond to dataset imbalances. Alarmingly, we find that none of the considered methods produces statistically fair and diverse results.

Despite its wide use in medicine, ultrasound imaging faces several challenges related to its poor signal-to-noise ratio and several sources of noise and artefacts. Enhancing ultrasound image quality involves balancing concurrent factors like contrast, resolution, and speckle preservation. In recent years, there has been progress both in model-based and learning-based approaches to improve ultrasound image reconstruction. Bringing the best from both worlds, we propose a hybrid approach leveraging advances in diffusion models. To this end, we adapt Denoising Diffusion Restoration Models (DDRM) to incorporate ultrasound physics through a linear direct model and an unsupervised fine-tuning of the prior diffusion model. We conduct comprehensive experiments on simulated, in-vitro, and in-vivo data, demonstrating the efficacy of our approach in achieving high-quality image reconstructions from a single plane wave input and in comparison to state-of-the-art methods. Finally, given the stochastic nature of the method, we analyse in depth the statistical properties of single and multiple-sample reconstructions, experimentally show the informativeness of their variance, and provide an empirical model relating this behaviour to speckle noise. The code and data are available at: (upon acceptance).

Ultrasound image reconstruction can be approximately cast as a linear inverse problem that has traditionally been solved with penalized optimization using the $l_1$ or $l_2$ norm, or wavelet-based terms. However, such regularization functions often struggle to balance the sparsity and the smoothness. A promising alternative is using learned priors to make the prior knowledge closer to reality. In this paper, we rely on learned priors under the framework of Denoising Diffusion Restoration Models (DDRM), initially conceived for restoration tasks with natural images. We propose and test two adaptions of DDRM to ultrasound inverse problem models, DRUS and WDRUS. Our experiments on synthetic and PICMUS data show that from a single plane wave our method can achieve image quality comparable to or better than DAS and state-of-the-art methods. The code is available at: https://github.com/Yuxin-Zhang-Jasmine/DRUS-v1.