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Density-Level Backward Error for Low-NFE Generative Flows

Ewsey R. Obzherin, Valentin Khrulkov · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.29475 · cited by 0 works (OpenAlex) · open-access PDF

Spanish

El muestreo de ODE generativo de bajo NFE está restringido no sólo por la orden del solvente, sino también por la forma en que se distribuye un presupuesto fijo de evaluaciones de red a lo largo del flujo. Desarrollamos un marco de error retroactivo de nivel de densidad que identifica el componente del defecto de la ecuación modificada de un solvente que cambia la margen evolutiva, excluyendo la distorsión de la trayectoria solenoide que es invisible en la geometría tangente fija de Wasserstein. El residuo resultante induce una regla de asignación de computación consciente del orden del solvente y, a través de la libertad de medición, un objetivo para seleccionar los representantes de velocidad favorables numéricamente de la misma ruta de densidad.

Machine translation (Meta M2M100); the English original follows.

Abstract

Low-NFE generative ODE sampling is constrained not only by solver order, but also by how a fixed budget of network evaluations is distributed along the flow. We develop a density-level backward-error framework that identifies the component of a solver's modified-equation defect that changes the evolving marginal, while excluding solenoidal trajectory distortion that is invisible in Wasserstein tangent geometry. The resulting residual induces a solver-order-aware compute-allocation rule and, through gauge freedom, an objective for selecting numerically favorable velocity representatives of the same density path. This separates our approach from schedule search driven by trajectory or endpoint surrogates and from higher-order solver design. Exact Gaussian and mixture models establish the mechanism, including cases where curvature-based allocation fails and continuum-optimal transport is not discretization-optimal. On a pretrained CIFAR-10 EDM probability-flow ODE, density-aware allocation consistently improves fixed-update Euler sampling in the low-NFE regime. Matched-seed convergence to a dense Euler reference confirms that the method accelerates approximation of the same high-NFE flow rather than changing the asymptotic sampler.

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Topics: Trajectory, Solver, Residual, Mathematics, Convergence (economics), Applied mathematics

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