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。所得常微分方程求解器的系数由微分方程公式、反向离散时间步长及所用微分方程方法预先确定。本文考虑通过改进积分近似优化特定系数以加速若干流行的基于微分方程的采样过程。在每个反向时间步长下，我们提出相对于某些选定系数最小化均方误差函数。该均方误差通过应用原始微分方程求解器在一组精细时间步长上构造，其原则上可在预测下一个扩散隐状态时提供更精确的积分近似。给定预训练的扩散模型，针对特定数量的神经函数评估的改进积分近似过程仅需对一批样本执行一次。通过最小均方误差获得的选定系数最优解可被保存并随后重复使用以加速采样过程。在EDM和DDIM上的大量实验表明，当神经函数评估数量较小时，改进积分近似技术能带来显著的性能提升。