  This paper introduces a novel deep-learning-based approach for numerical
simulation of a time-evolving Schr\"odinger equation inspired by stochastic
mechanics and generative diffusion models. Unlike existing approaches, which
exhibit computational complexity that scales exponentially in the problem
dimension, our method allows us to adapt to the latent low-dimensional
structure of the wave function by sampling from the Markovian diffusion.
Depending on the latent dimension, our method may have far lower computational
complexity in higher dimensions. Moreover, we propose novel equations for
stochastic quantum mechanics, resulting in quadratic computational complexity
with respect to the number of dimensions. Numerical simulations verify our
theoretical findings and show a significant advantage of our method compared to
other deep-learning-based approaches used for quantum mechanics.
