One popular diffusion-based sampling strategy attempts to solve the reverse ordinary differential equations (ODEs) effectively. The coefficients of the obtained ODE solvers are pre-determined by the ODE formulation, the reverse discrete timesteps, and the employed ODE methods. In this paper, we consider accelerating several popular ODE-based sampling processes by optimizing certain coefficients via improved integration approximation (IIA). At each reverse timestep, we propose to minimize a mean squared error (MSE) function with respect to certain selected coefficients. The MSE is constructed by applying the original ODE solver for a set of fine-grained timesteps which in principle provides a more accurate integration approximation in predicting the next diffusion hidden state. Given a pre-trained diffusion model, the procedure for IIA for a particular number of neural functional evaluations (NFEs) only needs to be conducted once over a batch of samples. The obtained optimal solutions for those selected coefficients via minimum MSE (MMSE) can be restored and reused later on to accelerate the sampling process. Extensive experiments on EDM and DDIM show the IIA technique leads to significant performance gain when the numbers of NFEs are small.

翻译：一种流行的基于扩散的采样策略试图有效求解反向常微分方程（ODE）。所获得的ODE求解器的系数由ODE公式、反向离散时间步长以及所采用的ODE方法预先确定。本文考虑通过改进积分近似（IIA）优化特定系数，以加速几种流行的基于ODE的采样过程。在每个反向时间步长中，我们提出针对所选系数最小化均方误差（MSE）函数。该MSE通过将原始ODE求解器应用于一组细粒度时间步长来构建，这在原理上为预测下一个扩散隐藏状态提供了更精确的积分近似。给定预训练扩散模型，针对特定数量的神经函数评估（NFE）的IIA过程仅需在一个样本批次上执行一次。通过最小均方误差（MMSE）获得的所选系数的最优解可被存储并随后重用，以加速采样过程。在EDM和DDIM上的广泛实验表明，当NFE数量较少时，IIA技术可带来显著的性能提升。