Interpreting and Improving Diffusion Models Using the Euclidean Distance Function

Denoising is intuitively related to projection. Indeed, under the manifold hypothesis, adding random noise is approximately equivalent to orthogonal perturbation. Hence, learning to denoise is approximately learning to project. In this paper, we use this observation to reinterpret denoising diffusion models as approximate gradient descent applied to the Euclidean distance function. We then provide straight-forward convergence analysis of the DDIM sampler under simple assumptions on the projection-error of the denoiser. Finally, we propose a new sampler based on two simple …

cs.cv cs.lg denoising diffusion diffusion models function gradient hypothesis indeed manifold math.oc noise observation paper project projection random stat.ml