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

By Sitan Chen, Sinho Chewi, Jungshian Li, Yuanzhi Li, Adil Salim, Anru R. Zhang. International Conference on Learning Representations, 2022

467 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/7309bf7607f4b4339f4ae288f3ad4fc36d139b5a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformers (2024, background): “Error bounds for SDE-based sampling with score-based diffusion models are studied in [13, 14, 37, 38].”
CoMoSpeech: One-Step Speech and Singing Voice Synthesis via Consistency Model (2023, background): “The issue that the model performance improves in a few sampling steps and then declines slightly as the number of steps increases is called the "sampling drift" challenge Daras et al. [2023] Ji et al. [2023] Chen et al.”
Stochastic Interpolants: A Unifying Framework for Flows and Diffusions (2023, methodology): “Control for SBDM-based techniques was later quantified more rigorously under the assumption of functional inequalities in a discretized setting by [25], which were removed by [26] and [9] via Girsanov-based techniques.”