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Diffusion probabilistic models (DPMs) are a powerful class of generative
models known for their ability to generate high-fidelity image samples. A major
challenge in the implementation of DPMs is the slow sampling process. In this
work, we bring a high-efficiency sampler for DPMs. Specifically, we propose a
score-based exact solution paradigm for the diffusion ODEs corresponding to the
sampling process of DPMs, which introduces a new perspective on developing
numerical algorithms for solving diffusion ODEs. To achieve an efficient
sampler, we propose a recursive derivative estimation (RDE) method to reduce
the estimation error. With our proposed solution paradigm and RDE method, we
propose the score-integrand solver with the convergence order guarantee as
efficient solver (SciRE-Solver) for solving diffusion ODEs. The SciRE-Solver
attains state-of-the-art (SOTA) sampling performance with a limited number of
score function evaluations (NFE) on both discrete-time and continuous-time DPMs
in comparison to existing training-free sampling algorithms. Such as, we
achieve $3.48$ FID with $12$ NFE and $2.42$ FID with $20$ NFE for
continuous-time DPMs on CIFAR10, respectively. Different from other samplers,
SciRE-Solver has the promising potential to surpass the FIDs achieved in the
original papers of some pre-trained models with just fewer NFEs. For example,
we reach SOTA value of $2.40$ FID with $100$ NFE for continuous-time DPM and of
$3.15$ FID with $84$ NFE for discrete-time DPM on CIFAR-10, as well as of
$2.17$ ($2.02$) FID with $18$ ($50$) NFE for discrete-time DPM on CelebA
64$\times$64.