Scalable quantum simulation of continuous-time generative models via tensor networks

Continuous-time flow and diffusion models are widely used across many application domains, from large-scale deployment in computer vision and protein folding to emerging adoption for modeling language, time series, and quantum states. After training, inferring statistical properties from continuous-time models is costly. Wavefunction flows target this cost by recasting learned transport as unitary evolution, whose final Born distribution approximates the target distribution. This prepares a coherent amplitude encoding (a qsample) that can be post-processed by quantum algorithms offering a quadratic advantage over Monte Carlo sampling. We present the first numerical study of these flows, in which we represent time-dependent potentials and states as tensor networks. At spatial dimension d=8, storage falls by sim 10^7times relative to the dense grid of N^d points, and evolution wall-clock time falls by gtrsim 10^3times against a baseline extrapolated from the measured dle 5 scaling. We validate our pipeline by reproducing the O\(1/sqrt{p_{rm rare}}\) scaling of rare-event sampling.