Why Fourier Space Reveals the Hidden Truth About Diffusion Models’ Detail Generation

Fourier Space Perspective on Diffusion Models: Why High-Frequency Detail Generation Matters 1. Fundamental Principles of Diffusion Models Diffusion models have revolutionized generative AI across domains like image synthesis, video generation, and protein structure prediction. These models operate through two key phases: 1.1 Standard DDPM Workflow Forward Process (Noise Addition): x_t = √(ᾱ_t)x_0 + √(1-ᾱ_t)ε Progressively adds isotropic Gaussian noise Controlled by decreasing noise schedule ᾱ_t Reverse Process (Denoising): Starts from pure noise (x_T ∼ N(0,I)) Uses U-Net to iteratively predict clean data 2. Key Insights from Fourier Analysis Transitioning to Fourier space reveals critical frequency-dependent behaviors: 2.1 Spectral Properties of Natural Data Data Type …