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Faster Diffusion Models via Higher-Order Approximation
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Faster Diffusion Models via Higher-Order Approximation
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In this paper, we explore provable acceleration of diffusion models without any additional retraining. Focusing on the task of approximating a target data distribution in $\mathbb{R}^d$ to within $\varepsilon$ total-variation distance, we propose a principled, training-free sampling algorithm that requires only the order of $$ d^{1+2/K} \varepsilon^{-1/K} $$ score function evaluations (up to log factor) in the presence of accurate scores, where $K>0$ is an arbitrary fixed integer. This result applies to a broad class of target data distributions, without the need for assumptions such as smoothness or log-concavity. Our theory is robust vis-a-vis inexact score estimation, degrading gracefully as the score estimation error increases -- without demanding higher-order smoothness on the score estimates as assumed in previous work. The proposed algorithm draws insight from high-order ODE solvers, leveraging high-order Lagrange interpolation and successive refinement to approximate the integral derived from the probability flow ODE. More broadly, our work develops a theoretical framework towards understanding the efficacy of high-order methods for accelerated sampling.
Forward citations
Cited by 7 Pith papers
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A Quantitative Approximation Framework for Flow Distillation in Diffusion Models
Develops error-propagation bounds and stability estimates for probability-flow ODE distillation, yielding a stability-balanced non-uniform time discretization that improves few-step sampling accuracy.
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Diffusion Models Adapt to Low-Dimensional Structure Under Flexible Coefficient Choices
For a broad class of coefficients, diffusion models achieve Õ(k/ε) iteration complexity for ε-accurate TV sampling under low-dimensional structure, independent of ambient dimension.
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Higher-order Diffusion Sampling via Chebyshev Interpolation and Gauss--Seidel Iterations
A Chebyshev-Gauss-Seidel higher-order sampler achieves d^{1+o(1)} ε^{-1/K} score complexity for TV distance ε under polynomial second-moment assumptions on the target.
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From Scores to Gibbs Correctors: Accelerating Uniform-Rate Discrete Diffusion Models
GADD achieves O(polylog(ε^{-1})) sampling complexity for uniform-rate discrete diffusion models via Gibbs correctors derived from the score function, with supporting experiments on text and music.
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On the Robustness of Distribution Support under Diffusion Guidance
Guided diffusion generates samples near the target distribution support under exact score access, explaining its empirical success in producing plausible outputs.
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Provable diffusion-based posterior sampling for linear inverse problems via DDIM
A SVD-based, coordinate-wise DDIM sampler is claimed to asymptotically sample from the posterior for noisy linear inverse problems, but the proof's posterior identification step does not follow from the stated updates.
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On the Robustness of Distribution Support under Diffusion Guidance
Establishes robustness of distribution support for guided diffusion processes under exact score access across DDIM, DDPM, and exponential integrator discretizations.
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