Chapter 22: Diffusion Models for Inverse Problems

Learning Objectives

• Understand the score function $\nabla_\mathbf{x}\log p(\mathbf{x})$ and its estimation via denoising score matching
• Derive the DDPM forward and reverse processes and connect noise prediction to score estimation
• Formulate Diffusion Posterior Sampling (DPS) and compute the likelihood guidance gradient via Tweedie's formula
• Compare measurement-consistent diffusion methods: DDRM, DDNM, MCG, DiffPIR
• Analyse the computational cost of diffusion-based reconstruction relative to PnP and unrolled methods
• Identify opportunities and challenges for applying diffusion models to RF imaging