Beyond Heat Dissipation: Optimizing Diffusion Models in Frequency Domain.

Area of Science:

• Artificial Intelligence
• Computer Vision
• Machine Learning

Background:

• Standard diffusion models often use pixel-wise degradations, ignoring image multi-scale characteristics.
• Generalized diffusion models with Positive Semi-definite Degradations (PSD) address this but face generation quality issues due to fixed inductive biases and incomplete optimization analysis.

Purpose of the Study:

• To provide a comprehensive theoretical analysis of the optimization process in the frequency domain for PSD-based generalized diffusion models.
• To propose a novel method that addresses the limitations of hand-crafted and fixed inductive biases in existing models.

Main Methods:

• Developed a theoretical analysis of the frequency domain optimization for PSD-based generalized diffusion models.
• Proposed the Frequency Inductive Biases Bootstrapping Optimization (FIBBO) method.
• FIBBO parameterizes the forward process and adaptively modifies the non-isotropic Gaussian kernel during training.

Main Results:

• Demonstrated that the forward process of PSD models implicitly influences inductive biases in the reverse process optimization.
• FIBBO enables learning distinct frequency degradation-generation trajectories iteratively.
• Experiments show significant improvements in generation quality for PSD-based generalized diffusion models.

Conclusions:

• FIBBO effectively tackles the limitations of hand-crafted and fixed inductive biases in PSD-based diffusion models.
• The adaptive nature of FIBBO enhances the model's performance across different data distributions.
• The proposed method offers a promising direction for improving generalized diffusion models.