Denoising diffusion probabilistic models (DDPMs) are a class of powerful
generative models. The past few years have witnessed the great success of DDPMs
in generating high-fidelity samples. A significant limitation of the DDPMs is
the slow sampling procedure. DDPMs generally need hundreds or thousands of
sequential function evaluations (steps) of neural networks to generate a
sample. This paper aims to develop a fast sampling method for DDPMs requiring
much fewer steps while retaining high sample quality. The inference process of
DDPMs approximates solving the corresponding diffusion ordinary differential
equations (diffusion ODEs) in the continuous limit. This work analyzes how the
backward error affects the diffusion ODEs and the sample quality in DDPMs. We
propose fast sampling through the \textbf{Restricting Backward Error schedule
(RBE schedule)} based on dynamically moderating the long-time backward error.
Our method accelerates DDPMs without any further training. Our experiments show
that sampling with an RBE schedule generates high-quality samples within only 8
to 20 function evaluations on various benchmark datasets. We achieved 12.01 FID
in 8 function evaluations on the ImageNet $128\times128$, and a $20\times$
speedup compared with previous baseline samplers.

本研究提出了一种基于 “限制后向误差进度表”（RBE 进度表）的快速采样方法，使 Denoising Diffusion Probabilistic Models（DDPM）拥有更快的采样速度而不需要进一步训练，并在各种基准数据集上实现了高品质图像的生成。

透过误差分析的角度快速扩散概率模型采样

Fast Diffusion Probabilistic Model Sampling through the lens of Backward  Error Analysis

Though denoising diffusion probabilistic models (DDPMs) have achieved
remarkable generation results, the low sampling efficiency of DDPMs still
limits further applications. Since DDPMs can be formulated as diffusion
ordinary differential equations (ODEs), various fast sampling methods can be
derived from solving diffusion ODEs. However, we notice that previous sampling
methods with fixed analytical form are not robust with the error in the noise
estimated from pretrained diffusion models. In this work, we construct an
error-robust Adams solver (ERA-Solver), which utilizes the implicit Adams
numerical method that consists of a predictor and a corrector. Different from
the traditional predictor based on explicit Adams methods, we leverage a
Lagrange interpolation function as the predictor, which is further enhanced
with an error-robust strategy to adaptively select the Lagrange bases with
lower error in the estimated noise. Experiments on Cifar10, LSUN-Church, and
LSUN-Bedroom datasets demonstrate that our proposed ERA-Solver achieves 5.14,
9.42, and 9.69 Fenchel Inception Distance (FID) for image generation, with only
10 network evaluations.

本文提出了一种基于 Adams 求解器和 Lagrange 插值的 ERA-Solver 方法，用于针对 DDPMs 中噪声估计的错误进行改进，该方法在图像生成方面取得了良好效果。