Accelerating Convergence of Score-Based Diffusion Models, Provably
| Autor: | Li, Gen, Huang, Yu, Efimov, Timofey, Wei, Yuting, Chi, Yuejie, Chen, Yuxin |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Score-based diffusion models, while achieving remarkable empirical performance, often suffer from low sampling speed, due to extensive function evaluations needed during the sampling phase. Despite a flurry of recent activities towards speeding up diffusion generative modeling in practice, theoretical underpinnings for acceleration techniques remain severely limited. In this paper, we design novel training-free algorithms to accelerate popular deterministic (i.e., DDIM) and stochastic (i.e., DDPM) samplers. Our accelerated deterministic sampler converges at a rate $O(1/{T}^2)$ with $T$ the number of steps, improving upon the $O(1/T)$ rate for the DDIM sampler; and our accelerated stochastic sampler converges at a rate $O(1/T)$, outperforming the rate $O(1/\sqrt{T})$ for the DDPM sampler. The design of our algorithms leverages insights from higher-order approximation, and shares similar intuitions as popular high-order ODE solvers like the DPM-Solver-2. Our theory accommodates $\ell_2$-accurate score estimates, and does not require log-concavity or smoothness on the target distribution. Comment: The first two authors contributed equally |
| Databáze: | arXiv |
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