Density-Level Backward Error for Low-NFE Generative Flows

Key points

• 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.1
• 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.1
• On a pretrained CIFAR-10 EDM probability-flow ODE, density-aware allocation consistently improves fixed-update Euler sampling in the low-NFE regime.1
• 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.1

Sources (1)

• [1]Density-Level Backward Error for Low-NFE Generative Flows
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 21, 09:30 AM

  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.

Extractive summary: sentences quoted from the sources.