The majority of standard diffusion models employ pixel-wise degradations while neglecting multi-scale characteristics of images. Recently, generalized diffusion models with Positive Semi-definite Degradations (PSD), such as heat dissipation and blurring, have been proposed to solve it, but suffering from problems of low generation quality due to incomplete optimization analysis and non-adaptiveness to the training process and different data distributions with hand-crafted and fixed inductive biases. In this paper, we present a comprehensive theoretical analysis of the optimization process in frequency domain for PSD-based generalized diffusion models, which implies the forward process of PSD frequency domain non-isotropic degradation implicitly acting on the inductive biases of the Variational Lower Bound non-isotropic weighting in the optimization reverse process. Based on this insight, we propose the Frequency Inductive Biases Bootstrapping Optimization (FIBBO) method, which parameterizes the forward process and learns distinct frequency degradation-generation trajectories iteratively. To tackle the problem of PSD hand-crafted and fixed inductive biases, FIBBO dynamically modifies the non-isotropic Gaussian kernel of the forward degradation process so that the inductive biases introduced can be adjusted adaptively during training. Experiments on public datasets show that FIBBO makes significant improvements in the generation quality of PSD-based generalized diffusion models. The code will be publicly available.
Wang et al. (Thu,) studied this question.