Diffusion Probabilistic Models (DPMs) have shown remarkable potential in image generation, but their sampling efficiency is hindered by the need for numerous denoising steps. Most existing solutions accelerate the sampling process by proposing fast ODE solvers. However, the inevitable discretization errors of the ODE solvers are significantly magnified when the number of function evaluations (NFE) is fewer. In this work, we propose PFDiff, a novel training-free and orthogonal timestep-skipping strategy, which enables existing fast ODE solvers to operate with fewer NFE. Specifically, PFDiff initially utilizes gradient replacement from past time steps to predict a "springboard". Subsequently, it employs this "springboard" along with foresight updates inspired by Nesterov momentum to rapidly update current intermediate states. This approach effectively reduces unnecessary NFE while correcting for discretization errors inherent in first-order ODE solvers. Experimental results demonstrate that PFDiff exhibits flexible applicability across various pre-trained DPMs, particularly excelling in conditional DPMs and surpassing previous state-of-the-art training-free methods. For instance, using DDIM as a baseline, we achieved 16.46 FID (4 NFE) compared to 138.81 FID with DDIM on ImageNet 64x64 with classifier guidance, and 13.06 FID (10 NFE) on Stable Diffusion with 7.5 guidance scale.

翻译：扩散概率模型在图像生成领域展现出卓越潜力，但其采样效率受限于大量去噪步骤的需求。现有加速方案多通过提出快速ODE求解器实现，然而当函数评估次数较少时，ODE求解器不可避免的离散化误差会被显著放大。本研究提出PFDiff——一种新颖的无训练正交时间步跳跃策略，使现有快速ODE求解器能够在更少的函数评估次数下运行。具体而言，PFDiff首先利用历史时间步的梯度替换预测"跳板"，随后结合受Nesterov动量启发的预见性更新机制，快速更新当前中间状态。该方法在有效减少不必要函数评估次数的同时，修正了一阶ODE求解器固有的离散化误差。实验结果表明，PFDiff在不同预训练扩散模型中均表现出灵活的适用性，尤其在条件扩散模型中表现卓越，超越了先前最先进的无训练方法。例如以DDIM为基线，在ImageNet 64x64数据集上使用分类器引导时，我们以4次函数评估获得16.46 FID（DDIM为138.81 FID）；在指导尺度为7.5的Stable Diffusion模型上以10次函数评估获得13.06 FID。