Gaussian Mixture Solvers for Diffusion Models
Hanzhong Guo Cheng Lu Fan Bao Tianyu Pang Shuicheng Yan Chao Du Chongxuan Li
Recently, diffusion models have achieved great success in generative tasks.
Sampling from diffusion models is equivalent to solving the reverse diffusion
stochastic differential equations (SDEs) or the corresponding probability flow
ordinary differential equations (ODEs). In comparison, SDE-based solvers can
generate samples of higher quality and are suited for image translation tasks
like stroke-based synthesis. During inference, however, existing SDE-based
solvers are severely constrained by the efficiency-effectiveness dilemma. Our
investigation suggests that this is because the Gaussian assumption in the
reverse transition kernel is frequently violated (even in the case of simple
mixture data) given a limited number of discretization steps. To overcome this
limitation, we introduce a novel class of SDE-based solvers called
\emph{Gaussian Mixture Solvers (GMS)} for diffusion models. Our solver
estimates the first three-order moments and optimizes the parameters of a
Gaussian mixture transition kernel using generalized methods of moments in each
step during sampling. Empirically, our solver outperforms numerous SDE-based
solvers in terms of sample quality in image generation and stroke-based
synthesis in various diffusion models, which validates the motivation and
effectiveness of GMS. Our code is available at
https://github.com/Guohanzhong/GMS.