发表机构
Université Paris Cité; CNRS; Heriot-Watt University; École Polytechnique; EPITA; Mohamed bin Zayed University of Artificial Intelligence（巴黎西岱大学; 法国国家科学研究中心; 赫瑞-瓦特大学; 巴黎综合理工学院; 法国计算机科学与技术高等学院; 穆罕默德·本·扎耶德人工智能大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文为多步一致性模型采样建立收敛理论，通过分离初始误差收缩与近似误差累积，推导出非渐近误差界，并指导采样器设计。
AI 中文摘要
一致性模型（CMs）已成为在少步数内生成高质量样本的领先方法。然而，增加步数可能会以高度依赖于调度且现有理论未能完全解释的方式提高或降低样本质量。为了提供准确性保证并指导CM采样器设计，我们将多步CM采样分析为加噪和近似去噪算子的组合。在明确、可验证的稳定性假设下，我们推导出一个非渐近误差界，该误差界将初始误差的收缩与近似误差的累积分离开来。该界为调度赋予了不同角色：较大的早期噪声水平驱动收缩，而较小的晚期噪声水平控制残余偏差。作为推论，我们获得了强对数凹和半对数凹目标的显式常数。我们进一步建立了一个互补性保证，其假设（一步准确性和稳定性）可以对给定的训练模型进行估计。实验表明，进入我们误差界的收缩和近似曲线可以被可靠地测量，并与预测的函数形式紧密匹配。总之，这些结果为多步CMs提供了有意义的收敛理论，并为采样器设计提供了实用途径。
英文摘要
Consistency models (CMs) have become a leading approach for generating high-quality samples in few steps. However, adding steps can improve or degrade sample quality in ways that are highly sensitive to the schedule and that existing theory does not fully explain. To provide accuracy guarantees and guide CM sampler design, we analyze multistep CM sampling as a composition of noising and approximate denoising operators. Under explicit, verifiable stability assumptions, we derive a non-asymptotic error bound that separates contraction of the initialization error from accumulation of approximation error. The bound assigns distinct roles to the schedule: large early noise levels drive contraction, while small late noise levels control the residual bias. As a corollary, we obtain explicit constants for strongly log-concave and semi-log-concave targets. We further establish a complementary guarantee whose assumptions, one-step accuracy and stability, can be estimated for a given trained model. Experiments show that the contraction and approximation profiles entering our bounds can be reliably measured and closely match the predicted functional forms. Together, these results provide a meaningful convergence theory for multi-step CMs and a practical route to sampler design.
Comments27 pages, 6 figures
