Unified Convergence Analysis for Score-Based Diffusion Models with Deterministic Samplers
Score-based diffusion models have emerged as powerful techniques for generating samples from high-dimensional data distributions. These models involve a two-phase process: first, injecting noise to transform the data distribution into a known prior distribution, and second, sampling to recover the original data distribution from noise. Among the various sampling methods, deterministic samplers stand out for their enhanced efficiency. However, analyzing these deterministic samplers presents unique challenges, as they preclude the use of established techniques such as Girsanov's theorem, which are only applicable to stochastic samplers. Furthermore, existing analysis for deterministic samplers usually focuses on specific examples, lacking a generalized approach for general forward processes and various deterministic samplers. Our paper addresses these limitations by introducing a unified convergence analysis framework. To demonstrate the power of our framework, we analyze the variance-preserving (VP) forward process with the exponential integrator (EI) scheme, achieving iteration complexity of $\tilde O(d^2/\epsilon)$. Additionally, we provide a detailed analysis of Denoising Diffusion Implicit Models (DDIM)-type samplers, which have been underexplored in previous research, achieving polynomial iteration complexity.
Code (0)
등록된 구현이 없습니다.
Tasks
DenoisingMethods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Convergence of Deterministic and Stochastic Diffusion-Model Samplers: A Simple Analysis in Wasserstein Distance
We provide new convergence guarantees in Wasserstein distance for diffusion-based generative models, covering both stochastic (DDPM-like) and deterministic (DDIM-like) sampling methods. We introduce a simple framework to…
A Recovery Theory for Diffusion Priors: Deterministic Analysis of the Implicit Prior Algorithm
Recovering high-dimensional signals from corrupted measurements is a central challenge in inverse problems. Recent advances in generative diffusion models have shown remarkable empirical success in providing strong data-…
Fast Convergence for High-Order ODE Solvers in Diffusion Probabilistic Models
Diffusion probabilistic models generate samples by learning to reverse a noise-injection process that transforms data into noise. Reformulating this reverse process as a deterministic probability flow ordinary differenti…
Numerical IntegrationA Unified Measure-Theoretic View of Diffusion, Score-Based, and Flow Matching Generative Models
We survey continuous-time generative modeling methods based on transporting a simple reference distribution to a data distribution via stochastic or deterministic dynamics. We present a unified framework in which diffusi…
The probability flow ODE is provably fast
We provide the first polynomial-time convergence guarantees for the probability flow ODE implementation (together with a corrector step) of score-based generative modeling. Our analysis is carried out in the wake of rece…
Denoising