Convergence of Deterministic and Stochastic Diffusion-Model Samplers: A Simple Analysis in Wasserstein Distance
This work addresses the need for rigorous theoretical analysis of diffusion model samplers, which is incremental as it builds on existing frameworks to refine error bounds and emphasize score function regularity.
The paper tackles the problem of analyzing convergence guarantees for diffusion-based generative models, providing new Wasserstein distance bounds for both stochastic and deterministic sampling methods, including the first such bound for the Heun sampler and improved results for the Euler sampler.
We provide new convergence guarantees in Wasserstein distance for diffusion-based generative models, covering both stochastic (DDPM-like) and deterministic (DDIM-like) sampling methods. We introduce a simple framework to analyze discretization, initialization, and score estimation errors. Notably, we derive the first Wasserstein convergence bound for the Heun sampler and improve existing results for the Euler sampler of the probability flow ODE. Our analysis emphasizes the importance of spatial regularity of the learned score function and argues for controlling the score error with respect to the true reverse process, in line with denoising score matching. We also incorporate recent results on smoothed Wasserstein distances to sharpen initialization error bounds.