Entropy-Based Dimension-Free Convergence and Loss-Adaptive Schedules for Diffusion Models

• URL: http://arxiv.org/abs/2601.21943v1
• Date: Thu, 29 Jan 2026 16:28:21 GMT
• Title: Entropy-Based Dimension-Free Convergence and Loss-Adaptive Schedules for Diffusion Models
• Authors: Ahmad Aghapour, Erhan Bayraktar, Ziqing Zhang,
• Abstract summary: Diffusion generative models synthesize samples by discretizing reverse-time dynamics driven by a learned score (or denoiser)<n>We develop an information-theoretic approach to dimension-free convergence that avoids geometric assumptions.<n>We also propose a Loss-Adaptive Schedule (LAS) for efficient discretization of reverse SDE which is lightweight and relies only on the training loss.
• Score: 3.2091923314854416
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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