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Provable Acceleration for Diffusion Models under Minimal Assumptions
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abstract
Score-based diffusion models, while achieving minimax optimality for sampling, are often hampered by slow sampling speeds due to the high computational burden of score function evaluations. Despite the recent remarkable empirical advances in speeding up the score-based samplers, theoretical understanding of acceleration techniques remains largely limited. To bridge this gap, we propose a novel training-free acceleration scheme for stochastic samplers. Under minimal assumptions -- namely, $L^2$-accurate score estimates and a finite second-moment condition on the target distribution -- our accelerated sampler provably achieves $\varepsilon$-accuracy in total variation within $\widetilde{O}(d^{5/4}/\sqrt{\varepsilon})$ iterations, thereby significantly improving upon the $\widetilde{O}(d/\varepsilon)$ iteration complexity of standard score-based samplers for $\varepsilon\leq 1/\sqrt{d}$. Notably, our convergence theory does not rely on restrictive assumptions on the target distribution or higher-order score estimation guarantees.
Forward citations
Cited by 10 Pith papers
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Low-dimensional adaptation of diffusion models: Convergence in total variation
Under exact score functions and a covering-number notion of intrinsic dimension, DDIM and DDPM reach TV error epsilon in O-tilde(k/epsilon) iterations.
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Faster Diffusion Models via Higher-Order Approximation
A new higher-order ODE sampler for diffusion models is proven to reach ε total-variation accuracy with eO(d^{1+2/K}/ε^{1/K}) iterations under mild assumptions.
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Almost Linear Convergence under Minimal Score Assumptions: Quantized Transition Diffusion
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Provable Efficiency of Guidance in Diffusion Models for General Data Distribution
For arbitrary data distributions, classifier-free guidance provably decreases the expected reciprocal classifier probability along the reverse diffusion process.
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Capturing Conditional Dependence via Auto-regressive Diffusion Models
Auto-regressive diffusion models provably control conditional-distribution sampling error with only a factor-K increase in inference cost, unlike vanilla diffusion where conditional error can blow up despite small joi...
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Information-Theoretic Proofs for Diffusion Sampling
Using information-theoretic identities, the authors prove non-asymptotic KL bounds for discrete-time diffusion sampling and show that matching higher moments accelerates convergence.
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