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We provide theoretical convergence guarantees for score-based generativemodels (SGMs) such as denoising diffusion probabilistic models (DDPMs), whichconstitute the backbone of large-scale real-world generative models such asDALL$\cdot$E 2. Our main result is that, assuming accurate score estimates,such SGMs can efficiently sample from essentially any realistic datadistribution. In contrast to prior works, our results (1) hold for an$L^2$-accurate score estimate (rather than $L^\infty$-accurate); (2) do notrequire restrictive functional inequality conditions that preclude substantialnon-log-concavity; (3) scale polynomially in all relevant problem parameters;and (4) match state-of-the-art complexity guarantees for discretization of theLangevin diffusion, provided that the score error is sufficiently small. Weview this as strong theoretical justification for the empirical success ofSGMs. We also examine SGMs based on the critically damped Langevin diffusion(CLD). Contrary to conventional wisdom, we provide evidence that the use of theCLD does not reduce the complexity of SGMs.

Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions