arXiv:2608.27216 2026 Sampling 1 ideas extracted · analyzed Aug 29, 2026
The paper turns generation into deterministic characteristic transport governed by a single initial phase, rather than learning an independently parameterized velocity field at every time. Its transferable asset is the Madelung decomposition: a probability density and phase are coupled by a continuity equation and a quantum-potential term proportional to the density's Fisher-information geometry. This suggests a phase-only generative flow in which a neural phase network is integrated through a constrained Hamiltonian PDE, with randomness used only to draw the initial latent particles. The most practical first test is a low-dimensional Eulerian or particle implementation on Gaussian and bimodal targets, where the method can be compared directly against flow matching and neural ODE baselines.
Replace a time-dependent neural velocity field with a neural initial phase whose evolution is determined by the Madelung equations. Particles are sampled once from a reference density and then moved deterministically along the characteristic velocity field, while the quantum potential supplies a density-dependent smoothing and curvature correction.