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Diffusion probabilistic models (DPMs) are emerging powerful generativemodels. Despite their high-quality generation performance, DPMs still sufferfrom their slow sampling as they generally need hundreds or thousands ofsequential function evaluations (steps) of large neural networks to draw asample. Sampling from DPMs can be viewed alternatively as solving thecorresponding diffusion ordinary differential equations (ODEs). In this work,we propose an exact formulation of the solution of diffusion ODEs. Theformulation analytically computes the linear part of the solution, rather thanleaving all terms to black-box ODE solvers as adopted in previous works. Byapplying change-of-variable, the solution can be equivalently simplified to anexponentially weighted integral of the neural network. Based on ourformulation, we propose DPM-Solver, a fast dedicated high-order solver fordiffusion ODEs with the convergence order guarantee. DPM-Solver is suitable forboth discrete-time and continuous-time DPMs without any further training.Experimental results show that DPM-Solver can generate high-quality samples inonly 10 to 20 function evaluations on various datasets. We achieve 4.70 FID in10 function evaluations and 2.87 FID in 20 function evaluations on the CIFAR10dataset, and a $4\sim 16\times$ speedup compared with previous state-of-the-arttraining-free samplers on various datasets.

DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps