Gaussian is All You Need: A Unified Framework for Solving Inverse Problems via Diffusion Posterior Sampling

Diffusion models can generate a variety of high-quality images by modeling complex data distributions. Trained diffusion models can also be very effective image priors for solving inverse problems. Most of the existing diffusion-based methods integrate data consistency steps within the diffusion reverse sampling process. The data consistency steps rely on an approximate likelihood function. In this paper, we show that the existing approximations are either insufficient or computationally inefficient. To address these issues, we propose a unified likelihood approximation method that incorporates a covariance correction term to enhance the performance and avoids propagating gradients through the diffusion model. The correction term, when integrated into the reverse diffusion sampling process, achieves better convergence towards the true data posterior for selected distributions and improves performance on real-world natural image datasets. Furthermore, we present an efficient way to factorize and invert the covariance matrix of the likelihood function for several inverse problems. We present comprehensive experiments to demonstrate the effectiveness of our method over several existing approaches.

Domain Expansion via Network Adaptation for Solving Inverse Problems

Deep learning-based methods deliver state-of-the-art performance for solving inverse problems that arise in computational imaging. These methods can be broadly divided into two groups: (1) learn a network to map measurements to the signal estimate, which is known to be fragile; (2) learn a prior for the signal to use in an optimization-based recovery. Despite the impressive results from the latter approach, many of these methods also lack robustness to shifts in data distribution, measurements, and noise levels. Such domain shifts result in a performance gap and in some cases introduce undesired artifacts in the estimated signal. In this paper, we explore the qualitative and quantitative effects of various domain shifts and propose a flexible and parameter efficient framework that adapt pretrained networks to such shifts. We demonstrate the effectiveness of our method for a number of natural image, MRI, and CT reconstructions tasks under domain, measurement model, and noise-level shifts. Our experiments demonstrate that our method provides significantly better performance and parameter efficiency compared to existing domain adaptation techniques.

Factorized Tensor Networks for Multi-Task and Multi-Domain Learning

Multi-task and multi-domain learning methods seek to learn multiple tasks/domains, jointly or one after another, using a single unified network. The key challenge and opportunity is to exploit shared information across tasks and domains to improve the efficiency of the unified network. The efficiency can be in terms of accuracy, storage cost, computation, or sample complexity. In this paper, we propose a factorized tensor network (FTN) that can achieve accuracy comparable to independent single-task/domain networks with a small number of additional parameters. FTN uses a frozen backbone network from a source model and incrementally adds task/domain-specific low-rank tensor factors to the shared frozen network. This approach can adapt to a large number of target domains and tasks without catastrophic forgetting. Furthermore, FTN requires a significantly smaller number of task-specific parameters compared to existing methods. We performed experiments on widely used multi-domain and multi-task datasets. We show the experiments on convolutional-based architecture with different backbones and on transformer-based architecture. We observed that FTN achieves similar accuracy as single-task/domain methods while using only a fraction of additional parameters per task.