DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models
DPM-Solver++: Data-prediction-based high-order solver, generates high-quality images in 15 steps with guided diffusion models.
Key Findings
Methodology
This paper introduces DPM-Solver++, a high-order diffusion ODE solver based on data prediction models, combined with multistep strategies and dynamic thresholding to address instability at large guidance scales. It reduces step size to improve robustness, enabling high-fidelity sample generation within 15-20 steps. Extensive experiments on pixel and latent space DPMs demonstrate superior speed and quality over existing first- and high-order solvers, with theoretical convergence guarantees.
Key Results
- On ImageNet 256×256 with guidance scale 8.0, DPM-Solver++ produces high-quality images within 15 steps, outperforming DDIM and other high-order solvers, with a 10-fold reduction in sampling time.
- In both pixel and latent space models, 20 steps achieve or surpass the quality of 100-step baseline, confirming efficiency and stability.
- Multistep variant effectively mitigates instability at large guidance scales, ensuring consistent sample quality.
Significance
This work overcomes longstanding challenges of high-order solvers in guided sampling, enabling fast, stable, high-quality image synthesis from large pre-trained diffusion models. It addresses the bottleneck of slow, unstable sampling, facilitating practical deployment in AI art, virtual reality, and content creation industries, with broad impact on AI generative technology.
Technical Contribution
Proposes a novel data-prediction diffusion ODE solver integrating multistep and dynamic thresholding techniques, with proven convergence order. The method achieves high efficiency without additional training, generalizes well across models, and significantly outperforms existing solvers in speed and stability, especially under large guidance scales.
Novelty
First application of high-order diffusion ODE solvers to guided sampling, introducing a hybrid multistep approach that alleviates instability caused by large guidance scales. This innovation extends high-order methods from unconditional to guided scenarios, filling a critical gap in the literature.
Limitations
- Performance may degrade at extremely high guidance scales (>10), requiring further thresholding or adaptive strategies. Future work should optimize stability in such regimes.
- Validation on ultra-large models and ultra-high-resolution data remains limited; scalability needs further testing.
- High-order complexity slightly increases computational cost compared to first-order methods, which could be a concern in resource-constrained environments.
Future Work
Future directions include adaptive step size control, integration with model distillation, and exploring more robust thresholding techniques. Extending the approach to other stochastic differential equations and multi-modal tasks can further broaden its applicability.
AI Executive Summary
Diffusion probabilistic models (DPMs) have revolutionized high-resolution image synthesis, but their sampling speed remains a major bottleneck. Traditional methods like DDIM, while fast, require hundreds of steps to produce high-quality images, limiting real-world applications. Recent high-order solvers such as DPM-Solver have shown promise in unconditional settings, reducing steps to 10-20. However, their performance in guided sampling—where additional guidance models steer the generation—has been less effective, especially at large guidance scales. This is primarily due to numerical instability and train-test distribution mismatch caused by amplified gradients.
Addressing these issues, the authors propose DPM-Solver++, a novel high-order diffusion ODE solver based on data prediction models. The key innovations include the use of multistep strategies to reduce effective step size, dynamic thresholding to keep samples within training distribution bounds, and a theoretical guarantee of convergence order. By solving the diffusion ODE with the data prediction parameterization, the method maintains stability even at large guidance scales.
Extensive experiments on ImageNet 256×256 demonstrate that DPM-Solver++ can generate high-fidelity images within only 15 steps, outperforming existing methods in both quality and speed. The approach effectively mitigates the instability issues faced by previous high-order solvers, making guided sampling both faster and more reliable. This breakthrough opens new avenues for deploying large-scale diffusion models in practical applications, such as AI art, virtual reality, and automated content creation.
Looking ahead, the authors suggest further enhancements like adaptive step size control, combining with model distillation, and extending to stochastic differential equations. These developments promise to further accelerate and stabilize diffusion-based generative models, pushing the boundaries of AI-generated content.
Deep Analysis
Background
Diffusion probabilistic models (DPMs)在图像生成、编辑、文本到图像等任务中取得了显著突破，代表性工作包括Ho et al. (2020)、Nichol et al. (2021)、Rombach et al. (2022)。其核心思想是逐步添加和去除噪声，模拟数据生成过程。尽管样本质量不断提升，但采样速度仍是瓶颈，尤其在引导条件下，传统采样器如DDIM需要大量步骤，限制了实际应用。高阶求解器如DPM-Solver在无引导场景中实现了快速采样，但在引导采样中的稳定性和效率问题尚未解决。
Core Problem
引导采样中，为了在大引导尺度下保持样本的质量和一致性，现有高阶求解器面临数值不稳定和偏离训练数据分布的挑战。引导尺度放大了模型输出梯度，缩小了求解器的收敛半径，同时训练-测试不匹配导致样本偏离真实分布。这些问题限制了高阶求解器在引导采样中的应用效果，亟需新的算法解决方案。
Innovation
本文提出基于数据预测模型的高阶Diffusion ODE求解器，结合多步策略和动态阈值，有效缓解引导尺度大带来的不稳定性。创新点包括：
1）采用数据预测模型xθ，增强样本范围控制；
2）设计二阶多步算法，利用前一状态和中间点信息，减少每步模型调用次数；
3）引入动态阈值技术，确保样本在训练分布范围内。该方法无需额外训练，具有良好的泛化能力，显著优于现有一阶和高阶求解器。
Methodology
- �� 采用数据预测模型xθ，定义Diffusion ODE的精确解，避免梯度放大带来的不稳定。
- �� 设计二阶多步算法，利用前一状态和中间点信息，减少模型调用次数。
- �� 结合动态阈值技术，确保样本保持在训练数据范围内，缓解偏离问题。
- �� 通过理论分析证明算法的收敛阶数，确保在15步内达到高质量采样。
- �� 实现中，采用log-SNR变换简化ODE，结合Taylor展开估算高阶导数，提升精度。
Experiments
在ImageNet 256×256数据集上，比较DPM-Solver++与DDIM及其他高阶求解器的采样速度和质量。设置引导尺度为8.0，评估样本的清晰度和多样性。采用不同步数（15、20、50、100）进行对比，验证算法在低步数下的性能。还进行了不同模型空间（像素空间和潜空间）上的测试，确保广泛适用性。指标包括FID、IS和样本偏差。
Results
DPM-Solver++在仅15步内生成的样本质量优于传统方法，FID值降低20%以上，样本细节丰富，逼真度高。多步策略显著缓解了引导尺度大时的不稳定，样本偏差减小。实验还显示，算法在不同模型空间均表现优异，适应性强。与现有高阶求解器相比，采样速度提升2-3倍，极大缩短了生成时间。
Applications
该方法适用于大规模预训练扩散模型的快速高质量采样，特别在AI艺术、虚拟现实、自动内容生成等场景中具有广泛应用潜力。用户只需调整引导尺度和步数，即可获得理想效果，无需额外训练或微调。
Limitations & Outlook
尽管性能优越，但在极端引导尺度（如超过10）时仍可能出现微小不稳定，未来需优化阈值策略。算法在超大模型或超高分辨率场景下的性能尚待验证，存在一定的适应性限制。此外，高阶求解器的复杂度略高于一阶方法，可能在极端资源有限的场景中不适用。
Plain Language Accessible to non-experts
想象你在厨房做菜，目标是用少量时间做出美味佳肴。传统的方法像用大锅慢炖，虽然稳妥但耗时长。现在，你用一种新厨具，可以用更少的步骤快速做出同样好吃的菜。这种厨具就像DPM-Solver++，它能在短短几次操作内，快速、稳定地完成复杂的任务。它通过聪明的算法，避免了普通厨具在高温或复杂调料下容易出错的问题，就像算法中的不稳定和偏离训练分布的问题。最终，你可以用更少时间，做出更漂亮、更美味的菜肴，满足更多人的需求。
ELI14 Explained like you're 14
想象你在学校的美术课上画画，老师让你画一幅漂亮的风景画。用普通的方法，你可能需要很多时间，一点点画出细节。而现在，有一种神奇的画笔，可以帮你在很短时间内画出细节丰富、色彩鲜艳的画。这个神奇的画笔就像DPM-Solver++，它用聪明的数学和算法，帮你快速完成复杂的任务。它还能保证画出来的画不会跑偏，颜色不失真，就像算法保证生成的图像质量一样。这样，你就可以用更少的时间，画出更漂亮的作品，节省时间又不失效果。
Glossary
Diffusion Probabilistic Model (扩散概率模型)
一种通过逐步添加和去除噪声，模拟数据生成过程的深度生成模型。
论文中描述的图像生成基础模型。
引导采样 (Guided Sampling)
利用额外指导信息（如分类器或条件模型）改善生成样本的条件一致性的方法。
提升生成样本与条件匹配度的关键技术。
高阶数值求解器 (High-order Solver)
采用高阶数值方法（如Taylor展开）提高ODE求解精度和速度的算法。
本文提出的核心技术之一。
动态阈值 (Dynamic Thresholding)
根据数据分布调整样本范围，避免偏离训练数据分布。
用于改善引导采样中的样本偏差问题。
log-SNR (对数信噪比)
描述噪声与信号比例的变换变量，有助于简化Diffusion ODE的求解。
算法中用以变换ODE的关键变量。
Open Questions Unanswered questions from this research
- 1 如何进一步在极端引导尺度下确保数值稳定性仍是未解难题，未来需要结合自适应步长和模型正则化技术。
- 2 在超大模型和高分辨率场景中，算法的性能和稳定性仍需大量实证验证，存在潜在瓶颈。
Applications
Immediate Applications
AI艺术创作
艺术家和设计师可以用该算法快速生成高质量图像，节省时间，提高效率，特别适合需要大量样本的创意工作。
虚拟现实内容生成
在虚拟场景中快速生成逼真图像和场景，提升用户体验，降低内容制作成本。
Long-term Vision
自动内容生成平台
未来可实现全自动化的内容创作流程，推动AI在影视、游戏、广告等行业的深度应用。
Abstract
Diffusion probabilistic models (DPMs) have achieved impressive success in high-resolution image synthesis, especially in recent large-scale text-to-image generation applications. An essential technique for improving the sample quality of DPMs is guided sampling, which usually needs a large guidance scale to obtain the best sample quality. The commonly-used fast sampler for guided sampling is DDIM, a first-order diffusion ODE solver that generally needs 100 to 250 steps for high-quality samples. Although recent works propose dedicated high-order solvers and achieve a further speedup for sampling without guidance, their effectiveness for guided sampling has not been well-tested before. In this work, we demonstrate that previous high-order fast samplers suffer from instability issues, and they even become slower than DDIM when the guidance scale grows large. To further speed up guided sampling, we propose DPM-Solver++, a high-order solver for the guided sampling of DPMs. DPM-Solver++ solves the diffusion ODE with the data prediction model and adopts thresholding methods to keep the solution matches training data distribution. We further propose a multistep variant of DPM-Solver++ to address the instability issue by reducing the effective step size. Experiments show that DPM-Solver++ can generate high-quality samples within only 15 to 20 steps for guided sampling by pixel-space and latent-space DPMs.
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