Convergence of the denoising diffusion probabilistic models for general noise schedules
This work presents a theoretical analysis of the original formulation of denoising diffusion probabilistic models (DDPMs), introduced by Ho, Jain, and Abbeel in Advances in Neural Information Processing Systems, 33 (2020), pp. 6840-6851. An explicit upper bound is derived for the total variation distance between the distribution of the discrete-time DDPM sampling algorithm and a target data distribution, under general noise schedule parameters. The analysis assumes certain technical conditions on the data distribution and a linear growth condition on the noise estimation function. The sampling sequence emerges as an exponential integrator-type approximation of a reverse-time stochastic differential equation (SDE) over a finite time interval. Schr\"odinger's problem provides a tool for estimating the distributional error in reverse time, which connects the reverse-time error with its forward-time counterpart. The score function in DDPMs appears as an adapted solution of a forward-backward SDE, providing a foundation for analyzing the time-discretization error associated with the reverse-time SDE.
Code (0)
등록된 구현이 없습니다.
Tasks
DenoisingNoise EstimationMethods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Mixed-State Quantum Denoising Diffusion Probabilistic Model
Generative quantum machine learning has gained significant attention for its ability to produce quantum states with desired distributions. Among various quantum generative models, quantum denoising diffusion probabilisti…
DenoisingmodelQuantum Machine LearningA Simple Analysis of Discretization Error in Diffusion Models
Diffusion models, formulated as discretizations of stochastic differential equations (SDEs), achieve state-of-the-art generative performance. However, existing analyses of their discretization error often rely on complex…
DenoisingBinary Diffusion Probabilistic Model
We introduce the Binary Diffusion Probabilistic Model (BDPM), a novel generative model optimized for binary data representations. While denoising diffusion probabilistic models (DDPMs) have demonstrated notable success i…
Blind Face RestorationDenoisingFacial InpaintingImage Generation+5Transformers Learn the Optimal DDPM Denoiser for Multi-Token GMMs
Transformer-based diffusion models have demonstrated remarkable performance at generating high-quality samples. However, our theoretical understanding of the reasons for this success remains limited. For instance, existi…
Rician Denoising Diffusion Probabilistic Models For Sodium Breast MRI Enhancement
Sodium MRI is an imaging technique used to visualize and quantify sodium concentrations in vivo, playing a role in many biological processes and potentially aiding in breast cancer characterization. Sodium MRI, however, …
DenoisingImage Quality Assessment