On the rate of convergence for score based diffusion models
Diffusion models are a new class of generative models that revolve around the estimation of the score function associated with a stochastic differential equation. Subsequent to its acquisition, the approximated score function is then harnessed to simulate the corresponding time-reversal process, ultimately enabling the generation of approximate data samples. In this talk, I will address the problem of establishing theoretical guarantees of convergence for diffusion models, that is to say the problem of estimating the distance between the output distribution and the sought data distribution. In order to do so, three sources of error need to be taken into account: the time-discretization error, the score-approximation error and the initialization error. I will illustrate the main ideas of a novel method based on the mixture of ideas coming from stochastic control and functional inequalities that allows to derive sharp convergence rates. Joint work with Giovanni Conforti and Alain Durmus.
Area: IS6 - Generative modelling and stochastic mass transport (Giovanni Conforti)
Keywords: Score Diffusion Models, Generative models, Convergence Bounds, Stochastic Control, Fisher Information
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