Adapt and Diffuse: Sample-adaptive Reconstruction via Latent Diffusion Models

Inverse problems arise in a multitude of applications, where the goal is to recover a clean signal from noisy and possibly (non)linear observations. The difficulty of a reconstruction problem depends on multiple factors, such as the structure of the ground truth signal, the severity of the degradation, the implicit bias of the reconstruction model and the complex interactions between the above factors. This results in natural sample-by-sample variation in the difficulty of a reconstruction task, which is often overlooked by contemporary techniques. Recently, diffusion-based inverse problem solvers have established new state-of-the-art in various reconstruction tasks. However, they have the drawback of being computationally prohibitive. Our key observation in this paper is that most existing solvers lack the ability to adapt their compute power to the difficulty of the reconstruction task, resulting in long inference times, subpar performance and wasteful resource allocation. We propose a novel method that we call severity encoding, to estimate the degradation severity of noisy, degraded signals in the latent space of an autoencoder. We show that the estimated severity has strong correlation with the true corruption level and can give useful hints at the difficulty of reconstruction problems on a sample-by-sample basis. Furthermore, we propose a reconstruction method based on latent diffusion models that leverages the predicted degradation severities to fine-tune the reverse diffusion sampling trajectory and thus achieve sample-adaptive inference times. We utilize latent diffusion posterior sampling to maintain data consistency with observations. We perform experiments on both linear and nonlinear inverse problems and demonstrate that our technique achieves performance comparable to state-of-the-art diffusion-based techniques, with significant improvements in computational efficiency.

DiracDiffusion: Denoising and Incremental Reconstruction with Assured Data-Consistency

Diffusion models have established new state of the art in a multitude of computer vision tasks, including image restoration. Diffusion-based inverse problem solvers generate reconstructions of exceptional visual quality from heavily corrupted measurements. However, in what is widely known as the perception-distortion trade-off, the price of perceptually appealing reconstructions is often paid in declined distortion metrics, such as PSNR. Distortion metrics measure faithfulness to the observation, a crucial requirement in inverse problems. In this work, we propose a novel framework for inverse problem solving, namely we assume that the observation comes from a stochastic degradation process that gradually degrades and noises the original clean image. We learn to reverse the degradation process in order to recover the clean image. Our technique maintains consistency with the original measurement throughout the reverse process, and allows for great flexibility in trading off perceptual quality for improved distortion metrics and sampling speedup via early-stopping. We demonstrate the efficiency of our method on different high-resolution datasets and inverse problems, achieving great improvements over other state-of-the-art diffusion-based methods with respect to both perceptual and distortion metrics. Source code and pre-trained models will be released soon.