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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

Korean

낮은 NFE 생성 ODE 샘플링은 솔버 순서뿐만 아니라 네트워크 평가의 고정 예산이 흐름을 따라 분포하는 방법에 의해 제한됩니다. 우리는 밀도 수준의 뒤로 실수 프레임 워크를 개발하여 솔버의 수정 된 균형 결함의 구성 요소를 식별하고 동일한 밀도 경로의 숫자적으로 유리한 속도 대표자를 선택하는 목표를 측정합니다. 이것은 Wasserstein의 고정 탱켄트 기하학에서 보이지 않는 솔로노이드 경로 왜곡을 제외합니다. 결과의 잔액은 솔버-order-aware-computing-allocation 규칙을 유도합니다. 정확한 가스 및 믹스 모델은 흐름 메커니즘을 구축하며, 곡선 기반의 모든 오프플

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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