This paper presents provably faster convergence rates for training-free deterministic and stochastic samplers in score-based diffusion models. The authors design novel training-free algorithms to accelerate popular deterministic (DDIM) and stochastic (DDPM) samplers. The accelerated deterministic sampler converges at a rate O(1/T²) with T the number of steps, improving upon the O(1/T) rate for the DDIM sampler. The accelerated stochastic sampler converges at a rate O(1/T), outperforming the O(1/√T) rate for the DDPM sampler. The design of these algorithms leverages insights from higher-order approximation and shares similar intuitions with popular high-order ODE solvers like DPM-Solver-2. The theory accommodates ℓ₂-accurate score estimates and does not require log-concavity or smoothness on the target distribution. Score-based diffusion models begin with a forward Markov diffusion process that progressively diffuses a data distribution into noise. The pivotal step is learning to construct a reverse Markov process using score functions. Mainstream approaches for constructing the reverse-time process can be divided into two categories: stochastic (or SDE-based) samplers and deterministic (or ODE-based) samplers. DDIM converges more rapidly than DDPM, although DDPM produces more diverse data instances. Theoretical analysis for diffusion-based generative modeling is still in its early stages. Recent works have explored the convergence rate of the data generating process in a non-asymptotic fashion. Chen et al. (2022) proved that the iteration complexity of the DDPM sampler is proportional to 1/ε². Li et al. (2023) demonstrated that its iteration complexity scales proportionally to 1/ε allowing score estimation error. Deterministic samplers often exhibit faster convergence in both practice and theory. Acceleration is a key challenge in diffusion generative modeling. While distillation-based techniques have achieved outstanding empirical performance, they often necessitate additional training processes. An alternative route towards acceleration is "training-free," which directly invokes the pre-trained diffusion model for sampling without requiring additional training processes. Examples of training-free accelerated samplers include DPM-Solver, DPM-Solver++, DEIS, UniPC, and SA-Solver. In this paper, the authors answer the question of whether we can design a training-free deterministic (resp. stochastic) sampler that converges provably faster than the DDIM (resp. DDPM). In the deterministic setting, they demonstrate how to speed up the ODE-based sampler (i.e., the DDIM-type sampler). The proposed sampler, which exploits some sort of momentum term to adjust the update rule, leverages insights from higher-order ODE approximation in discrete time and shares similar intuitions with the fast ODE-based sampler DPM-Solver-2. They establish non-asymptotic convergence guarantees for the accelerated DDIM-type sampler, showingThis paper presents provably faster convergence rates for training-free deterministic and stochastic samplers in score-based diffusion models. The authors design novel training-free algorithms to accelerate popular deterministic (DDIM) and stochastic (DDPM) samplers. The accelerated deterministic sampler converges at a rate O(1/T²) with T the number of steps, improving upon the O(1/T) rate for the DDIM sampler. The accelerated stochastic sampler converges at a rate O(1/T), outperforming the O(1/√T) rate for the DDPM sampler. The design of these algorithms leverages insights from higher-order approximation and shares similar intuitions with popular high-order ODE solvers like DPM-Solver-2. The theory accommodates ℓ₂-accurate score estimates and does not require log-concavity or smoothness on the target distribution. Score-based diffusion models begin with a forward Markov diffusion process that progressively diffuses a data distribution into noise. The pivotal step is learning to construct a reverse Markov process using score functions. Mainstream approaches for constructing the reverse-time process can be divided into two categories: stochastic (or SDE-based) samplers and deterministic (or ODE-based) samplers. DDIM converges more rapidly than DDPM, although DDPM produces more diverse data instances. Theoretical analysis for diffusion-based generative modeling is still in its early stages. Recent works have explored the convergence rate of the data generating process in a non-asymptotic fashion. Chen et al. (2022) proved that the iteration complexity of the DDPM sampler is proportional to 1/ε². Li et al. (2023) demonstrated that its iteration complexity scales proportionally to 1/ε allowing score estimation error. Deterministic samplers often exhibit faster convergence in both practice and theory. Acceleration is a key challenge in diffusion generative modeling. While distillation-based techniques have achieved outstanding empirical performance, they often necessitate additional training processes. An alternative route towards acceleration is "training-free," which directly invokes the pre-trained diffusion model for sampling without requiring additional training processes. Examples of training-free accelerated samplers include DPM-Solver, DPM-Solver++, DEIS, UniPC, and SA-Solver. In this paper, the authors answer the question of whether we can design a training-free deterministic (resp. stochastic) sampler that converges provably faster than the DDIM (resp. DDPM). In the deterministic setting, they demonstrate how to speed up the ODE-based sampler (i.e., the DDIM-type sampler). The proposed sampler, which exploits some sort of momentum term to adjust the update rule, leverages insights from higher-order ODE approximation in discrete time and shares similar intuitions with the fast ODE-based sampler DPM-Solver-2. They establish non-asymptotic convergence guarantees for the accelerated DDIM-type sampler, showing