# QonFusion -- Quantum Approaches to Gaussian Random Variables: Applications in Stable Diffusion and Brownian Motion

arXiv: https://arxiv.org/abs/2309.16258 · HTML: https://mlsanity.com/paper/2309.16258/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 52 references that are in the map.
- First posted on arXiv 28 Sep 2023.

## Builds on (most cited first, 23 of 23)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [Understanding Diffusion Models: A Unified Perspective](https://mlsanity.com/paper/2208.11970/) (2022)
- [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019)
- [Differentiable Learning of Quantum Circuit Born Machine](https://mlsanity.com/paper/1804.04168/) (2018)
- [A Morphology Focused Diffusion Probabilistic Model for Synthesis of Histopathology Images](https://mlsanity.com/paper/2209.13167/) (2022)
- [SeqDiffuSeq: Text Diffusion with Encoder-Decoder Transformers](https://mlsanity.com/paper/2212.10325/) (2022)
- [Diffusion Models for Constrained Domains](https://mlsanity.com/paper/2304.05364/) (2023)
- [Quantum Generative Models for Small Molecule Drug Discovery](https://mlsanity.com/paper/2101.03438/) (2021)
- [How Much is Enough? A Study on Diffusion Times in Score-based Generative Models](https://mlsanity.com/paper/2206.05173/) (2022)
- [ConsistencyTTA: Accelerating Diffusion-Based Text-to-Audio Generation with Consistency Distillation](https://mlsanity.com/paper/2309.10740/) (2023)
- [ADIR: Adaptive Diffusion for Image Reconstruction](https://mlsanity.com/paper/2212.03221/) (2022)
- [Exploring the Optimal Choice for Generative Processes in Diffusion Models: Ordinary vs Stochastic Differential Equations](https://mlsanity.com/paper/2306.02063/) (2023)
- [TransFusion: Transcribing Speech with Multinomial Diffusion](https://mlsanity.com/paper/2210.07677/) (2022)
- [Further scramblings of Marsaglia's xorshift generators](https://mlsanity.com/paper/1404.0390/) (2014)
- [On testing pseudorandom generators via statistical tests based on the arcsine law](https://mlsanity.com/paper/1903.09805/) (2019)
- [A supplemental investigation of non-linearity in quantum generative models with respect to simulatability and optimization](https://mlsanity.com/paper/2302.00788/) (2023)

## Built on by (most cited first, 1 of 1)

- [PixelBoost: Leveraging Brownian Motion for Realistic-Image Super-Resolution](https://mlsanity.com/paper/2506.23254/) (2025)

## Abstract (arXiv)

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 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 urlhttps://boltzmannentropy.github.io/qonfusion.github.io/ to reproduce all findings here.