# Learning to Integrate Diffusion ODEs by Averaging the Derivatives Source: [Learning to Integrate Diffusion ODEs by Averaging the Derivatives]() Collection index: [llms.txt]() Data updated: 2025-12-17T05:02:44.796Z Authors: Wenze Liu, Xiangyu Yue Published: 2025-05-20T15:30:38.000Z ## Abstract To accelerate diffusion model inference, numerical solvers perform poorly at extremely small steps, while distillation techniques often introduce complexity and instability. This work presents an intermediate strategy, balancing performance and cost, by learning ODE integration using loss functions derived from the derivative-integral relationship, inspired by Monte Carlo integration and Picard iteration. From a geometric perspective, the losses operate by gradually extending the tangent to the secant, thus are named as secant losses. The target of secant losses is the same as that of diffusion models, or the diffusion model itself, leading to great training stability. By fine-tuning or distillation, the secant version of EDM achieves a $10$-step FID of $2.14$ on CIFAR-10, while the secant version of SiT-XL/2 attains a $4$-step FID of $2.27$ and an $8$-step FID of $1.96$ on ImageNet-$256\\times256$. Code is available at https://github.com/poppuppy/secant-expectation. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Class-conditional image generation on ImageNet 256x256 (val)](): Class-conditional Image Generation; ImageNet 256x256 (val); Inception Score (IS): not recorded. ## Original sources and implementation [Original paper]() [PDF]()