Solving Inverse Problems using Diffusion with Iterative Colored Renoising.

Area of Science:

• Artificial Intelligence
• Computer Vision
• Image Processing

Background:

• Unsupervised imaging inverse problems can be solved using pre-trained diffusion models.
• This requires approximating the gradient of the measurement-conditional score function during the diffusion reverse process.
• Existing approximation methods show poor performance, particularly early in the reverse process.

Purpose of the Study:

• To develop a novel approach for improving the accuracy and efficiency of solving imaging inverse problems with diffusion models.
• To address the limitations of existing score function approximation methods.
• To introduce a new iterative re-estimation and re-noising technique.

Main Methods:

• Propose Fast Iterative REnoising (FIRE), an iterative method that re-estimates and re-noises estimates multiple times per diffusion step.
• FIRE injects shaped colored noise to ensure the diffusion model consistently receives white noise, aligning with its training.
• Embed FIRE into the DDIM reverse process to create a new method called DDfire.

Main Results:

• DDfire demonstrates state-of-the-art accuracy and runtime performance on various linear inverse problems.
• DDfire achieves excellent results in phase retrieval tasks.
• The proposed FIRE method significantly improves upon existing score function approximation techniques.

Conclusions:

• The FIRE approach offers a substantial improvement for unsupervised solving of imaging inverse problems using diffusion models.
• DDfire provides a computationally efficient and highly accurate solution for tasks like phase retrieval.
• The developed method enhances the compatibility of pre-trained diffusion models with the demands of inverse problem-solving.