To smooth a cloud or to pin it down: Guarantees and Insights on Score Matching in Denoising Diffusion Models
This work addresses theoretical gaps in diffusion models for researchers, but it is incremental as it builds on existing connections to stochastic control.
The paper tackles the problem of providing theoretical guarantees for denoising diffusion models by extending neural network approximation results from the Föllmer drift to these models, resulting in new insights and guarantees for score matching.
Denoising diffusion models are a class of generative models which have recently achieved state-of-the-art results across many domains. Gradual noise is added to the data using a diffusion process, which transforms the data distribution into a Gaussian. Samples from the generative model are then obtained by simulating an approximation of the time reversal of this diffusion initialized by Gaussian samples. Recent research has explored adapting diffusion models for sampling and inference tasks. In this paper, we leverage known connections to stochastic control akin to the Föllmer drift to extend established neural network approximation results for the Föllmer drift to denoising diffusion models and samplers.