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The probability flow ODE is provably fast
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abstract
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 recent results obtaining such guarantees for the SDE-based implementation (i.e., denoising diffusion probabilistic modeling or DDPM), but requires the development of novel techniques for studying deterministic dynamics without contractivity. Through the use of a specially chosen corrector step based on the underdamped Langevin diffusion, we obtain better dimension dependence than prior works on DDPM ($O(\sqrt{d})$ vs. $O(d)$, assuming smoothness of the data distribution), highlighting potential advantages of the ODE framework.
Forward citations
Cited by 3 Pith papers
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Denoising growth complexity: Data geometry and certified schedules for diffusion sampling
A new measure, the denoising growth complexity, provides local KL error bounds for Euler diffusion samplers and yields certified, geometry-adaptive schedules.
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Fast Score-Based Sampling via Log-Concave Reductions
Score-based sampling reduces to a short sequence of strongly log-concave sampling problems, giving √d polylog(1/ε) complexity bounds and logarithmic dependence on the condition number for log-concave targets.
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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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