AI and the World's Hard Problems · Theoretical computer science · arXiv · 2026-10-22
Density-Level Backward Error for Low-NFE Generative Flows
When generative ODEs are sampled with a small budget of network evaluations (low NFE), performance is constrained not only by solver order but by how that fixed budget is distributed along the flow. The authors develop a density-level backward-error framework that identifies the component of a solver's modified-equation defect that changes the evolving marginal, yielding a solver-order-aware compute-allocation rule and, through gauge freedom, an objective for selecting numerically favorable velocity representatives of the same density path. Exact Gaussian and mixture models establish the mechanism, and on a pretrained CIFAR-10 EDM probability-flow ODE, density-aware allocation consistently improves fixed-update Euler sampling in the low-NFE regime while converging to the same dense Euler reference.