Polynomial Speedup in Diffusion Models with the Multilevel Euler-Maruyama Method

Diffusion models have achieved remarkable success in generating high-fidelity content but suffer from slow, iterative sampling, resulting in high latency that limits their use in interactive applications. We introduce DRiffusion, a parallel sampling framework that parallelizes diffusion inference through a draft-and-refine process. DRiffusion employs skip transitions to generate multiple draft states for future timesteps and computes their corresponding noises in parallel, which are then used in the standard denoising process to produce refined results. Theoretically, our method achieves an acceleration rate of $\tfrac{1}{n}$ or $\tfrac{2}{n+1}$, depending on whether the conservative or aggressive mode is used, where $n$ denotes the number of devices. Empirically, DRiffusion attains 1.4$\times$-3.7$\times$ speedup across multiple diffusion models while incur minimal degradation in generation quality: on MS-COCO dataset, both FID and CLIP remain largely on par with those of the original model, while PickScore and HPSv2.1 show only minor average drops of 0.17 and 0.43, respectively. These results verify that DRiffusion delivers substantial acceleration and preserves perceptual quality.

Discrete diffusion models have achieved strong empirical performance in text and other symbolic domains, with masked (absorbing-rate) variants emerging as competitive alternatives to autoregressive models. Among existing samplers, the Euler method remains the standard choice in many applications, and more recently, the First-Hitting Sampler (FHS) has shown considerable promise for masked diffusion models. Despite their practical success, the theoretical understanding of these samplers remains limited. Existing analyses are conducted in Kullback-Leibler (KL) divergence, which often yields loose parameter dependencies and requires strong assumptions on score estimation. Moreover, these guarantees do not cover recently developed high-performance sampler of FHS. In this work, we first develop a direct total-variation (TV) based analysis for the Euler method that overcomes these limitations. Our results relax assumptions on score estimation, improve parameter dependencies, and establish convergence guarantees without requiring any surrogate initialization. Also for this setting, we provide the first convergence lower bound for the Euler sampler, establishing tightness with respect to both the data dimension $d$ and the target accuracy $\varepsilon$. Finally, we analyze the FHS sampler and show that it incurs no sampling error beyond that induced by score estimation, which we show to be tight with a matching lower error bound. Overall, our analysis introduces a direct TV-based error decomposition along the CTMC trajectory and a decoupling-based path-wise analysis for FHS, which may be of independent interest.

Diffusion models achieve state-of-the-art generative performance but suffer from high computational costs during inference due to the repeated evaluation of a heavy neural network. In this work, we propose Dual-Rate Diffusion, a method to accelerate sampling by interleaving the execution of a heavy high-capacity context encoder and a light efficient denoising model. The context encoder is evaluated sparsely to extract high-dimensional features, which are effectively reused by the light denoising model at every step to refine the sample efficiently. This approach significantly accelerates inference without compromising sample quality. On ImageNet benchmarks, Dual-Rate Diffusion matches the performance of standard baselines while reducing computational cost by a factor of $2$-$4$. Furthermore, we demonstrate that our method is compatible with distillation techniques, such as Moment Matching Distillation, enabling further efficiency gains in few-step generation.