Diffusion Model Based Posterior Sampling for Noisy Linear Inverse Problems
This work addresses a computational bottleneck for researchers and practitioners using generative models in tasks like super-resolution and denoising, though it is incremental as it builds on existing frameworks.
The paper tackles the slow inference time of diffusion-based methods for noisy linear inverse problems by proposing a closed-form approximation to the likelihood score, achieving competitive or better reconstruction performance while being significantly faster than baselines.
With the rapid development of diffusion models and flow-based generative models, there has been a surge of interests in solving noisy linear inverse problems, e.g., super-resolution, deblurring, denoising, colorization, etc, with generative models. However, while remarkable reconstruction performances have been achieved, their inference time is typically too slow since most of them rely on the seminal diffusion posterior sampling (DPS) framework and thus to approximate the intractable likelihood score, time-consuming gradient calculation through back-propagation is needed. To address this issue, this paper provides a fast and effective solution by proposing a simple closed-form approximation to the likelihood score. For both diffusion and flow-based models, extensive experiments are conducted on various noisy linear inverse problems such as noisy super-resolution, denoising, deblurring, and colorization. In all these tasks, our method (namely DMPS) demonstrates highly competitive or even better reconstruction performances while being significantly faster than all the baseline methods.