提出轻量级神经求解器SpanLift，提升生成ODE采样效率。
Learning to Solve Generative ODEs Beyond the Linear Span
- 通过空间残差项突破线性跨度限制，增强求解精度
- 3次模型评估即达CIFAR-10 FID 5.69，ImageNet FID 11.83
- 兼容预训练模型，适配扩散与流模型采样任务
扩散与流生成模型通过积分学习到的常微分方程（ODE）进行采样，但高质量生成仍需大量序列模型评估。求解器学习通过调整标量系数、时间步长或两者来降低计算成本，同时保持主干模型不变。本文识别出该方法族中的结构瓶颈：每一步更新仍受限于缓冲速度向量的线性跨度。由于标量系数更新仅位于缓冲速度的线性张量内，只能拟合张量内的分量，无法通过标量重组捕捉张量外的残差。为此，提出SpanLift，一种轻量级神经求解器，在标量系数更新基础上引入空间残差算子。SpanLift以固定基求解器作为张量内先验，学习状态与速度缓冲上的空间残差算子，通过终点教师匹配训练，保留预训练主干模型且不增加模型评估次数（NFE）。实验表明，学习到的修正项可跨基求解器迁移，且主要为张量外成分。在像素空间扩散、潜在流匹配及降水预报任务中，SpanLift实现少步采样的最新性能。仅用3次NFE，CIFAR-10 FID从8.16降至5.69，ImageNet FID从17.37降至11.83。
原文摘要 · Abstract (English)
Diffusion and flow generative models sample by integrating a learned ODE, but high quality still requires many sequential model evaluations. Solver learning reduces this cost by adapting scalar coefficients, timesteps, or both, while keeping the backbone model fixed. In this work, we identify a structural bottleneck in this update family: each step remains span-limited. Since the scalar-coefficient update lies in the span of buffered velocity evaluations, it can fit only the in-span component while leaving any out-of-span residual unreachable by scalar recombination alone. We propose SpanLift, a lightweight neural solver that augments scalar-coefficient updates with a spatial residual operator. SpanLift keeps a fixed base solver as an in-span prior and learns a spatial residual operator over the state and velocity buffer. The operator is trained by endpoint teacher matching, preserves the pretrained backbone, and adds no model NFEs. Empirically, the learned correction transfers across base solvers and is predominantly out-of-span. Across pixel-space diffusion, latent flow matching, and precipitation nowcasting, SpanLift achieves state-of-the-art few-step sampling. With only 3 NFE, it improves CIFAR-10 FID from 8.16 to 5.69 and ImageNet FID from 17.37 to 11.83.
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