I-SplineFlow: Learning Monotone Spline Stochastic Interpolant Schedulers for Few-Step Generation

Abstract

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 B\'ezier 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 B\'ezier 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.