Diffusion generative models synthesize samples by discretizing reverse-time dynamics driven by a learned score (or denoiser). Existing convergence analyses of diffusion models typically scale at least linearly with the ambient dimension, and sharper rates often depend on intrinsic-dimension assumptions or other geometric restrictions on the target distribution. We develop an alternative, information-theoretic approach to dimension-free convergence that avoids any geometric assumptions. Under mild assumptions on the target distribution, we bound KL divergence between the target and generated distributions by $O(H^2/K)$ (up to endpoint factors), where $H$ is the Shannon entropy and $K$ is the number of sampling steps. Moreover, using a reformulation of the KL divergence, we propose a Loss-Adaptive Schedule (LAS) for efficient discretization of reverse SDE which is lightweight and relies only on the training loss, requiring no post-training heavy computation. Empirically, LAS improves sampling quality over common heuristic schedules.

翻译：扩散生成模型通过离散化由学习到的评分（或去噪器）驱动的逆时间动力学来合成样本。现有扩散模型的收敛性分析通常至少与环境维度呈线性比例关系，且更尖锐的收敛率往往依赖于目标分布的内在维度假设或其他几何限制。我们提出了一种替代性的、基于信息论的无维度收敛方法，避免了任何几何假设。在目标分布的温和假设下，我们将目标分布与生成分布之间的KL散度上界控制在$O(H^2/K)$（忽略端点因子），其中$H$为香农熵，$K$为采样步数。此外，通过重新表述KL散度，我们提出了一种用于高效离散化反向随机微分方程的自适应损失调度方法。该方法计算轻量，仅依赖于训练损失，无需训练后的繁重计算。实验表明，相较于常见的启发式调度方法，自适应损失调度能提升采样质量。