I-SplineFlow：学习用于少步生成的单调样条随机插值调度器
I-SplineFlow: Learning Monotone Spline Stochastic Interpolant Schedulers for Few-Step Generation
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中文总结 AI 辅助
提出I-SplineFlow，用积分单调样条参数化随机插值调度器，实现扩散与流模型的少步生成，在低NFE下改善FID，且训练仅需数分钟。
中文摘要 AI 辅助
通过轻量级训练优化采样轨迹而非网络，可以加速预训练扩散模型和流模型的少步生成。近期一种方法将随机插值（SI）调度器参数化为一条平滑曲线，其控制点强制执行SI调度器必须满足的三个性质：固定边界条件、单调信噪比（SNR）和可微性。现有参数化使用全局支持的多项式基，其中每个控制点都会移动整条曲线，更高的表达能力需要更高的次数，这会在优化过程中耦合调度中相距较远的区域。我们引入了I-SplineFlow，它使用积分单调样条（I样条）对调度器进行参数化。I样条将多项式次数与混合权重的数量解耦，因此可以在固定权重数量下为每个模型选择支持宽度和平滑度，并且紧支撑的导数基使调度器的雅可比矩阵的条件数比Bézier基好几个数量级。边界条件和严格单调的SNR通过构造得到保证，参数上没有排序约束，且速度导数具有闭式形式。在扩散（EDM）和流（ReFlow、Simple ReFlow）模型中，I-SplineFlow在大多数设置下改善了少步FID，尤其是在最低NFE时最为明显，并且训练只需几分钟。消融实验表明，次数自由度和单调性约束都是必需的。代码将在接收后发布。
英文摘要
Few-step generation with pretrained diffusion and flow models can be accelerated by lightweight training that optimizes the sampling trajectory rather than the network. A recent approach parameterizes the stochastic interpolant (SI) scheduler as a smooth curve whose control points enforce the three properties an SI scheduler must satisfy: fixed boundary conditions, a monotone signal-to-noise ratio (SNR), and differentiability. Existing parameterizations use globally supported polynomial bases, where every control point moves the whole curve and higher expressiveness needs a higher degree, which couples distant regions of the schedule during optimization. We introduce \emph{I-SplineFlow}, which parameterizes the scheduler with integrated monotone splines (I-splines). I-splines decouple the polynomial degree from the number of mixture weights, so support width and smoothness can be chosen per model at a fixed weight count, and the compactly supported derivative basis makes the scheduler Jacobian orders of magnitude better conditioned than a Bézier basis. Boundary conditions and a strictly monotone SNR hold by construction, with no ordering constraint on the parameters and closed-form velocity derivatives. Across diffusion (EDM) and flow (ReFlow, Simple ReFlow) models, I-SplineFlow improves few-step FID over Bézier scheduling in most settings, most clearly at the lowest NFEs, and trains in minutes. Ablations show that both the degree freedom and the monotonicity constraint are needed. The code will be released upon acceptance.
