Removing Structured Noise with Diffusion Models
This work addresses inverse problems with non-Gaussian measurement models, offering practical applications in domains like imaging or signal processing, though it is incremental as it builds on existing diffusion model paradigms.
The paper tackles the problem of solving ill-posed inverse problems with structured noise by extending diffusion models to include rich noise models, resulting in strong performance gains that outperform competitive baselines using normalizing flows and adversarial networks.
Solving ill-posed inverse problems requires careful formulation of prior beliefs over the signals of interest and an accurate description of their manifestation into noisy measurements. Handcrafted signal priors based on e.g. sparsity are increasingly replaced by data-driven deep generative models, and several groups have recently shown that state-of-the-art score-based diffusion models yield particularly strong performance and flexibility. In this paper, we show that the powerful paradigm of posterior sampling with diffusion models can be extended to include rich, structured, noise models. To that end, we propose a joint conditional reverse diffusion process with learned scores for the noise and signal-generating distribution. We demonstrate strong performance gains across various inverse problems with structured noise, outperforming competitive baselines that use normalizing flows and adversarial networks. This opens up new opportunities and relevant practical applications of diffusion modeling for inverse problems in the context of non-Gaussian measurement models.