  In the present study, we delineate a strategy focused on non-parametric
quantum circuits for the generation of Gaussian random variables (GRVs). This
quantum-centric approach serves as a substitute for conventional pseudorandom
number generators (PRNGs), such as the \textbf{torch.rand} function in PyTorch.
The principal theme of our research is the incorporation of Quantum Random
Number Generators (QRNGs) into classical models of diffusion. Notably, our
Quantum Gaussian Random Variable Generator fulfills dual roles, facilitating
simulations in both Stable Diffusion (SD) and Brownian Motion (BM). This
diverges markedly from prevailing methods that utilize parametric quantum
circuits (PQCs), often in conjunction with variational quantum eigensolvers
(VQEs). Although conventional techniques can accurately approximate ground
states in complex systems or model elaborate probability distributions, they
require a computationally demanding optimization process to tune parameters.
Our non-parametric strategy obviates this necessity. To facilitate assimilating
our methodology into existing computational frameworks, we put forward
QonFusion, a Python library congruent with both PyTorch and PennyLane,
functioning as a bridge between classical and quantum computational paradigms.
We validate QonFusion through extensive statistical testing, including tests
which confirm the statistical equivalence of the Gaussian samples from our
quantum approach to classical counterparts within defined significance limits.
QonFusion is available at
\url{https://boltzmannentropy.github.io/qonfusion.github.io/} to reproduce all
findings here.
