Generative processes that involve solving differential equations, such as diffusion models, frequently necessitate balancing speed and quality. ODE-based samplers are fast but plateau in performance while SDE-based samplers deliver higher sample quality at the cost of increased sampling time. We attribute this difference to sampling errors: ODE-samplers involve smaller discretization errors while stochasticity in SDE contracts accumulated errors. Based on these findings, we propose a novel sampling algorithm called Restart in order to better balance discretization errors and contraction. The sampling method alternates between adding substantial noise in additional forward steps and strictly following a backward ODE. Empirically, Restart sampler surpasses previous SDE and ODE samplers in both speed and accuracy. Restart not only outperforms the previous best SDE results, but also accelerates the sampling speed by 10-fold / 2-fold on CIFAR-10 / ImageNet $64 \times 64$. In addition, it attains significantly better sample quality than ODE samplers within comparable sampling times. Moreover, Restart better balances text-image alignment/visual quality versus diversity than previous samplers in the large-scale text-to-image Stable Diffusion model pre-trained on LAION $512 \times 512$. Code is available at https://github.com/Newbeeer/diffusion_restart_sampling

翻译：涉及解微分方程的生成过程（如扩散模型）通常需要在速度与质量之间取得平衡。基于ODE的采样器速度快但性能存在平台期，而基于SDE的采样器能以增加采样时间为代价获得更高的样本质量。我们将这种差异归因于采样误差：ODE采样器涉及较小的离散化误差，而SDE中的随机性则能收缩累积误差。基于这些发现，我们提出了一种名为Restart的新型采样算法，以更好地平衡离散化误差与误差收缩。该采样方法交替执行在额外前向步中添加大量噪声与严格遵循反向ODE的操作。实验表明，Restart采样器在速度和精度上均超越了先前的SDE和ODE采样器。Restart不仅优于之前最优的SDE结果，还在CIFAR-10 / ImageNet $64 \times 64$上将采样速度提升了10倍/2倍。此外，在相近采样时间内，它获得的样本质量显著优于ODE采样器。在基于LAION $512 \times 512$预训练的大规模文生图Stable Diffusion模型中，Restart比先前采样器更好地平衡了文本-图像对齐/视觉质量与多样性之间的关系。代码开源于 https://github.com/Newbeeer/diffusion_restart_sampling