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

Understand

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.