A popular approach to sample a diffusion-based generative model is to solve an ordinary differential equation (ODE). In existing samplers, the coefficients of the 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 (including EDM, DDIM, and DPM-Solver) by optimizing certain coefficients via improved integration approximation (IIA). We propose to minimize, for each time step, a mean squared error (MSE) function with respect to the 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 state. The proposed IIA technique does not require any change of a pre-trained model, and only introduces a very small computational overhead for solving a number of quadratic optimization problems. Extensive experiments show that considerably better FID scores can be achieved by using IIA-EDM, IIA-DDIM, and IIA-DPM-Solver than the original counterparts when the neural function evaluation (NFE) is small (i.e., less than 25).

翻译：一种流行的扩散生成模型采样方法是求解常微分方程（ODE）。在现有采样器中，ODE求解器的系数由ODE公式、反向离散时间步长及所采用的ODE方法预先确定。本文考虑通过改进积分逼近（IIA）优化特定系数，以加速多种主流基于ODE的采样过程（包括EDM、DDIM和DPM-Solver）。我们提出在每个时间步中，针对所选系数最小化均方误差（MSE）函数。该MSE通过应用原始ODE求解器对一组细粒度时间步长进行计算构建，该原理上能在预测下一个扩散状态时提供更精确的积分逼近。所提出的IIA技术无需对预训练模型进行任何修改，仅需极小的计算开销求解一系列二次优化问题。大量实验表明，当神经函数评估（NFE）次数较少时（即小于25次），采用IIA-EDM、IIA-DDIM和IIA-DPM-Solver可取得显著优于原始版本的FID分数。