Assessing the Quality of Denoising Diffusion Models in Wasserstein Distance: Noisy Score and Optimal Bounds
This work provides theoretical insights into the robustness of diffusion models, which is incremental but important for practitioners in generative modeling.
The paper tackles the problem of quantifying the robustness and convergence rates of denoising diffusion probabilistic models (DDPMs) to noisy score estimates, establishing finite-sample guarantees in Wasserstein-2 distance that show faster convergence and optimality matching Gaussian case rates.
Generative modeling aims to produce new random examples from an unknown target distribution, given access to a finite collection of examples. Among the leading approaches, denoising diffusion probabilistic models (DDPMs) construct such examples by mapping a Brownian motion via a diffusion process driven by an estimated score function. In this work, we first provide empirical evidence that DDPMs are robust to constant-variance noise in the score evaluations. We then establish finite-sample guarantees in Wasserstein-2 distance that exhibit two key features: (i) they characterize and quantify the robustness of DDPMs to noisy score estimates, and (ii) they achieve faster convergence rates than previously known results. Furthermore, we observe that the obtained rates match those known in the Gaussian case, implying their optimality.