LEAP: Accelerating ODE-based Diffusion Sampling with Optimal Linear Leaps

Sampling from a diffusion model typically requires many forward passes through a large neural network, making generation computationally expensive. While much work has focused on efficient solvers and samplers, comparatively little attention has been paid to selecting the sampling timesteps themselves. A recent line of work optimizes theoretically derived surrogates for sample quality rather than the quality metric itself. We propose Optimizing Your Sampling (OYS), which instead treats timestep selection as a black-box optimization problem, optimizing the target metric directly with Bayesian optimization. OYS outperforms both the default schedules and those of Align Your Steps on text-to-image generation, and improves over the default schedules on inpainting and other image tasks, in both quantitative and human evaluations. OYS requires no additional training, is applicable even to distilled models, and improves both simple and sophisticated samplers such as Euler and DPM-Solver++. A 5-step OYS schedule retains 89%-94% of the quality of a 50-step schedule while reducing inference cost by 10x.

Text-to-image diffusion models have achieved unprecedented success but still struggle to produce high-quality results under limited sampling budgets. Existing training-free sampling acceleration methods are typically developed independently, leaving the overall performance and compatibility among these methods unexplored. In this paper, we bridge this gap by systematically elucidating the design space, and our comprehensive experiments identify the sampling time schedule as the most pivotal factor. Inspired by the geometric properties of diffusion models revealed through the Frenet-Serret formulas, we propose constant total rotation schedule (TORS), a scheduling strategy that ensures uniform geometric variation along the sampling trajectory. TORS outperforms previous training-free acceleration methods and produces high-quality images with 10 sampling steps on Flux.1-Dev and Stable Diffusion 3.5. Extensive experiments underscore the adaptability of our method to unseen models, hyperparameters, and downstream applications. Code is available at https://github.com/zju-pi/TORS.

Diffusion and flow matching models generate high-quality samples, but their ODE samplers often need tens to hundreds of neural function evaluations (NFEs). This remains a practical challenge for released checkpoints, since many accelerators require additional design choices and training cost through retraining, distillation, or trajectory redesign. We investigate a different route based on $x$-prediction. During sampling, standard affine probability paths already expose $x_0$ information: an intermediate state and its path velocity determine a principled estimate of the clean sample. We formalize this property as endpoint decodability and show that the decoder is the minimum-MSE estimator $\mathbb{E}[x_0\mid x_t]$ under the usual $\ell_2$ objective. This yields Truncated Jump Sampling (TJS): stop the ODE at an early-exit time $t^*$ and return the decoded $x_0$. TJS requires no retraining, distillation, or architecture change. Across SDXL, SD3.5M, Z-Image-Turbo, and three class-conditional benchmarks, it reduces NFEs by 20--70% with near-matched quality. The analysis also shows why endpoint prediction can work without straightening the trajectory, providing inference acceleration without trajectory redesign.